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Financial Mathematics

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A savings account earns compound interest at 1.5% per month.
Calculate the equivalent annual rate of interest

", "licence": "None specified"}, "statement": "

A savings account earns compound interest at a rate of $\\var{perc}$% per quarter.
Calculate the Annual Percentage Rate (APR).

$\\ APR = (1+i)^n-1 $

", "advice": "

The quarterly interest rate is $\\var{perc}$% per quarter. There are 4 quarters in one year so the equivalent annual rate of interest can be calculated as follows:

$APR=(1+\\frac{\\var{perc}}{100})^{4}-1=\\var{apr2}-1=\\var{apr}$

Therefore the APR is $\\var{perc2}$%

Please give your answer as a percentage correct to two decimal places.

[[0]]%

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Write your answer as a percentage.

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A credit card company charges compound interest at x% per month
on unpaid balances.

", "licence": "None specified"}, "statement": "

A credit card company charges compound interest at a rate of $\\var{perc}$% per month on unpaid balances.

$\\ APR = (1+i)^n-1 $

", "advice": "

The monthly interest rate is $\\var{perc}$% per month. There are 12 months in one year so the APR can be calculated as follows:

$APR=(1+\\frac{\\var{perc}}{100})^{12}-1=\\var{apr2}-1=\\var{apr}$

Therefore the APR is $\\var{perc2}$%

Calculate the Annual Percentage Rate (APR) for this credit card. Please give your answer as a percentage correct to two decimal places.

[[0]]%

Write your answer as a percentage.

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An investor puts €$\\var{A0}$ in a banks saving account with a fixed interest rate earning compound interest. In return they receive €$\\var{A}$ in $\\var{n}$ years time.

The compound interest formula is:

$\\ A = P(1+i)^n $

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Calculate the annual interest rate.

Please give your answer as a percentage correct to 3 decimal places.

[[0]]%

Write your answer as a percentage.

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To provide for retirement an employee deposits R at the end of each month in an account that earns $perc% annual interest compound monthly. What is the future value of the annuity in nyears?

", "licence": "None specified"}, "statement": "

To provide for retirement an employee deposits €$\\var{R}$ at the end of each month into an account that earns $\\var{perc}$% annual interest compounded monthly.

", "advice": "

The future value of an annuity, $A$ is given by:

$A=\\frac{R[(1+i)^n-1]}{i}$

where $R$ represents the periodic payment, $i$ represents the interest rate per period and $n$ represents the number of payments.

$A$ represents the future value of the annuity, this is what we are asked to calculate.

$i$ represents the rate of compound interest. the annual interest rate is $\\var{perc}$% so the monthly rate of interest is $\\frac {\\var{perc}} {12}=\\var{perc2}$% and therefore $i=\\frac{\\var{perc2}}{100}=\\var{int}$.

$n$ represents the number of payments, there are 12 payments over $\\var{years}$ year(s) so $n$ is $12 \\times \\var{years}=\\var{n}$.

The value of each repayment, is €$\\var{R}$

Using the formula:

$A=\\frac{R[(1+i)^n-1]}{i}$

$A=\\frac{\\var{R}[(1+\\var{int})^{\\var{n}}-1]}{\\var{int}}$

$A=\\frac{\\var{R}[\\var{num}-1]}{\\var{int}}$

$A=\\frac{\\var{R}[\\var{num2}]}{\\var{int}}$

$A = \\var{R} \\times \\var{num3}$

$A=\\var{A}$

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Which formula should we use to calculate the future value of the annuity in $\\var{years}$ years?

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What is the future value of the annuity in $\\var{years}$ years?

€[[0]]

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The future value of an annuity, $A$ is given by:

$A=R\\left[\\frac{(1+i)^n-1}{i}\\right]$

where $R$ represents the periodic payment, $i$ represents the interest rate per period and $n$ represents the number of payments.

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A pharmaceutical company wishes to accumulate €$\\var{A}$ to upgrade its manufacturing plant in $3$ years time.

", "licence": "None specified"}, "statement": "

A pharmaceutical company wishes to accumulate €$\\var{A}$ to upgrade its manufacturing plant. The upgrade is due to be paid for on December 31st 2017 so the company makes three equal deposits into a savings account earning compound interest at a rate of $\\var{perc}$% per annum. The payments are made on 31st December 2015, 31st December 2016 and 31st December 2017.

", "advice": "

Since the payments are made at the end of the year, the formula for calculating the future value ($A$) of an annuity is given by:

$A=\\frac{R[(1+i)^{n}-1]}{i}$

where $R$ represents the periodic payment, $i$ represents the interest rate per period and $n$ represents the number of payments.

Part (a)

$A$ represents the future value of the annuity, this is the amount to be saved, therefore $A=€\\var{A}$

Part (b)

$i$ represents the rate of compound interest, the annual interest rate is $\\var{perc}$% so $i$ is $\\frac {\\var{perc}} {100}=\\var{int}$.

Part(c)

$n$ represents the number of payments , so $n$ is $\\var{n}$.

Part (d)

The value of each repayment, €$R$ can be calculated using the future value formula or it can be calculated directly by calculating the amount of interest that each deposit earns.Using the formula:

$A=\\frac{R[(1+i)^{n}-1]}{i}$

$\\var{A}=\\frac{R[(1+\\var{int})^{\\var{n}}-1]}{\\var{int}}$

$\\var{A}=\\frac{R[\\var{num}-1]}{\\var{int}}$

$\\var{A}=\\frac{R[\\var{num2}]}{\\var{int}}$

$\\var{A} = R \\times \\var{num3}$

$\\frac{\\var{A}}{\\var{num3}}=R$

$\\var{R}=R$

Alternatively, we can calculate $R$ directly:

The amount to be saved is €$\\var{A}$ so $A=\\var{A}$. The interest rate per annum is $\\var{int}$ and there are $n$ repayments so $n=\\var{n}$.

The future value of the deposit made on 31st December 2015 is: $R \\times (1+\\var{int})^2$
The future value of the deposit made on 31st December 2016 is: $R\\times(1+\\var{int})$
Thevalue of the deposit made on 31st December 2016 is: $R$

Thus the future value is given by:

$A=R\\times(1+\\var{int})^2$+$R\\times(1+\\var{int})$+$R$

$\\var{A}=R\\times(1+\\var{int})^2$+$R\\times(1+\\var{int})$+$R$

$\\var{A}=R[(1+\\var{int})^2$+$(1+\\var{int})+1$

$\\var{A}=R[\\var{frac2}+\\var{frac1}+1]$

$\\var{A} = R \\times \\var{num4}$

$\\frac{\\var{A}}{\\var{num4}}=R$

$\\var{R}=R$

Part (e)

The amount of interest paid is the difference between the amount accumulated ($A$) and the three deposits of €$\\var{R}$

Interest = $\\var{A}- 3 \\times \\var{R}=\\var{Interest}$

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Which formula should we use to calculate how large each deposit should be?

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What is the value of $A$?

€[[0]]

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What is the value of $i$?

[[0]]

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What is the value of $n$?

[[0]]

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Calculate how large each deposit will need to be.

Please give your answer to the nearest cent.

€[[0]]

Since the payments are made at the end of the year, the formula for calculating the future value ($A$) of an annuity is:

$A=R\\left[\\frac{(1+i)^{n}-1}{i}\\right]$

where $R$ represents the value of the regular deposit, $i$ represents the interest rate and $n$ represents the number of payments.

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Calculate the total amount of interest that the company will earn over the three years.

Please give your answer to the nearest cent.

€[[0]]

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The principal, $P$, is the €[[0]] lent to the individual.

The final amount, $A$, is the €[[1]] paid back.

Since the individual has paid back €[[2]] more that s\\he borrowed, this is the interest.

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A bank lends an individual £$\\var{capital}$. The individual has to pay back the bank £$\\var{interest}$ in $\\var{n}$ years time.

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Compare two loans with different interest rates.

", "licence": "None specified"}, "statement": "

Two rival high street banks offer customers a new loan.

Bank A offers a loan at a rate of $\\var{perc1}$% per annum where interest is compounded annually.

Bank B offers a loan at a rate of $\\var{perc2}$% per annum where interest is compounded monthly.

Suppose that a potential customer wishes to borrow €$\\var{P}$ for $\\var{n1}$ years.

The compound interest formula is:

$\\ A = P(1+i)^n $

", "advice": "

The compound interest formula is: $\\ A = P(1+i)^n $

Part (a)

n represents the number of compounding periods , so for Bank A it is $\\var{n1}$ years.

i represents the rate of compound interest, for Bank A, the annual interest rate is $\\var{perc1}$% so i is $\\frac {\\var{perc1}} {100}=\\var{int1}$.

The amount owed to Bank A after $\\var{n1}$ years is denoted by A. Using the compound interest formula:

$A=P(1+i)^n$

$A=\\var{P} \\times(1+\\var{int1})^\\var{n1}=\\var{A1}$

The amount of interest accumulated over the $\\var{n1}$ years is the difference between the amount borrowed ($P$) and the amount payed back ($A$).

$A-P=\\var{A1}-\\var{P}=\\var{I1}$

Part(b)

n represents the number of compounding periods. For Bank B interest is compounded monthly for $\\var{n1}$ years so there are a total of $12 \\times \\var{n1} =\\var{n2}$ compounding periods.

i represents the rate of compound interest. For Bank B, the interest rate is ${\\var{perc2}}$% per annum compounded monthly.

The interest rate per month is $\\frac{\\var{perc2}}{12}=\\var{int3}$%

Therefore $i=\\frac{\\var{int3}}{100}=\\var{int2}$

The amount owed to Bank A after $\\var{n1}$ years is denoted by A. Using the compound interest formula:

$A=P(1+i)^n$

$A=\\var{P} \\times(1+\\var{int2})^\\var{n2}=\\var{A2}$

The amount of interest accumulated over the $\\var{n1}$ years is the difference between the amount borrowed ($P$) and the amount payed back ($A$).

$A-P=\\var{A2}-\\var{P}=\\var{I2}$

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Suppose that the potential customer chooses Bank A.

What is the value of $n$?

[[0]]

What is the value of $i$ as a decimal?

[[1]]

At the end of the $\\var{n1}$ years, how much must the customer pay to Bank A to clear the loan?

Please give your answer to the nearest cent.

€[[2]]

How much interest does the loan accumulate during the $\\var{n1}$ years?

Please give your answer to the nearest cent.

€[[3]]

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Suppose that the potential customer chooses Bank B.

What is the value of $n$?

[[0]]

What is the value of $i$? Please include all the decimal places in your answer.

[[1]]

At the end of the $\\var{n1}$ years, how much must the customer pay to Bank B to clear the loan?

Please give your answer to the nearest cent.

€[[2]]

How much interest does the loan accumulate during the $\\var{n1}$ years?

Please give your answer to the nearest cent.

€[[3]]

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An investment of €x invested today will give a return of €y in n years time Calculate the net present value (NPV) of the investment given that the discount rate is 3.5% per annum.

", "licence": "None specified"}, "statement": "

An investment will give a return of €$\\var{Return1}$ in $\\var{n1}$ years time.

The formula for calculating the present value of an investment is:

$P=\\frac{A}{(1+i)^n}$

", "advice": "

We wish to calculate the present value of an investment that will be worth €$\\var{Return1}$ in $\\var{n1}$ years time. Using the present value formula:

$P=\\frac{A}{(1+i)^{n}}$

where $A$ is €$\\var{Return1}$, $n$ is $\\var{n1}$ and $i$ is $\\frac{\\var{perc}}{100}=\\var{int}$ gives:

$P=\\frac{\\var{Return1}}{(1+\\var{int})^{\\var{n1}}}$

$P=\\frac{\\var{Return1}}{\\var{num}}$

$P=\\var{NPV}$

Calculate the present value of the investment given that the discount rate is $\\var{perc}$% per annum. Round your answer to the nearest cent.

€[[0]]

An investment of x invested today will give a return of €y in n1 years time and a further €z n2 years from today. Calculate the net present value (NPV) of the investment given that the discount rate is perc% per annum.

", "licence": "None specified"}, "statement": "

An investment of €$\\var{Invest}$ invested today will give a return of €$\\var{Return1}$ in $\\var{n1}$ years' time and a further return of €$\\var{Return2}$ in $\\var{n2}$ years' time. The discount rate is $\\var{perc}$% per annum.

The formula for calculating the present value of an investment is:

$P=\\frac{A}{(1+i)^n}$

Round each answer to 2 decimal places.

", "advice": "

We wish to calculate the net present value (NPV) of an investment that will be worth €$\\var{Return1}$ in $\\var{n1}$ years time plus an additional €$\\var{Return2}$ in $\\var{n2}$ years time. Using the present value formula, the present value of the €$\\var{Return1}$ is:

$P=\\frac{A}{(1+i)^{n}}$

where $A$ is €$\\var{Return1}$, $n$ is $\\var{n1}$ and $i$ is $\\frac{\\var{perc}}{100}=\\var{int}$

$P1=\\frac{\\var{Return1}}{(1+\\var{int})^{\\var{n1}}}$

$P1=\\frac{\\var{Return1}}{\\var{num}}$

$P1=\\var{PV1}$

Using the present value formula, the present value of the €$\\var{Return2}$ is:

$P=\\frac{A}{(1+i)^{n}}$

where $A$ is €$\\var{Return2}$, $n$ is $\\var{n2}$ and $i$ is $\\frac{\\var{perc}}{100}=\\var{int}$

$P2=\\frac{\\var{Return2}}{(1+\\var{int})^{\\var{n2}}}$

$P2=\\frac{\\var{Return2}}{\\var{num}}$

$P2=\\var{PV2}$

The NPV of the total amount is $P1+P2 - Investment =\\var{PV1}+\\var{PV2}-\\var{Invest}=€\\var{NPV}$

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The present value of a return of €$\\var{Return1}$ in $\\var{n1}$ years time is:

€[[0]]

The present value of a return of €$\\var{Return2}$ in $\\var{n2}$ years time is:

€[[0]]

Calculate the net present value (NPV) of the investment.

€[[0]]

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The loan must be repaid to the bank in three equal repayments
Calculate:
(i) how large each repayment will need to be
(ii) the total amount of interest that the company will pay to the bank over the four years.

", "licence": "None specified"}, "statement": "

On January 1, 2015 a company borrowed €$\\var{P}$ from a bank at $\\var{perc}$% per annum compound interest. The loan must be repaid to the bank in three equal repayments, due on December 31 in 2015, 2016 and 2017.

", "advice": "

The present value of an annuity, $P$ is given by:

$P=\\frac{R[1-(1+i)^{-n}]}{i}$

where $R$ represents the periodic payment, $i$ represents the interest rate per period and $n$ represents the number of payments.

Part (a)

$P$ represents the present value of the annuity, this is the amount borrowed, therefore $P=€\\var{P}$

Part (b)

$i$ represents the rate of compound interest, the annual interest rate is $\\var{perc}$% so $i$ is $\\frac {\\var{perc}} {100}=\\var{int}$.

Part(c)

$n$ represents the number of payments , so $n$ is $\\var{n}$.

Part (d)

The value of each repayment, €$R$ can be calculated using the present value formula or it can be calculated directly by discounting each payment according to how far into the future it lies.

Using the formula:

$P=\\frac{R[1-(1+i)^{-n}]}{i}$

$\\var{P}=\\frac{R[1-(1+\\var{int})^{-\\var{n}}]}{\\var{int}}$

$\\var{P}=\\frac{R[1-\\var{num}]}{\\var{int}}$

$\\var{P}=\\frac{R[\\var{num2}]}{\\var{int}}$

$\\var{P} = R \\times \\var{num3}$

$\\frac{\\var{P}}{\\var{num3}}=R$

$\\var{R}=R$

Alternatively, we can calculate $R$ directly:

The principle borrowed from the bank is €$\\var{P}$ so $P=\\var{P}$. The interest rate per annum is $\\var{int}$ and there are $n$ repayments so $n=\\var{n}$.

The present value of the first repayment is: $\\frac{R}{(1+\\var{int})}$
The present value of the second repayment is: $\\frac{R}{(1+\\var{int})^2}$
The present value of the third repayment is: $\\frac{R}{(1+\\var{int})^3}$

Thus the present value is given by:

$P=\\frac{R}{(1+\\var{int})}$+$\\frac{R}{(1+\\var{int})^2}$+$\\frac{R}{(1+\\var{int})^3}$

$\\var{P}=\\frac{R}{(1+\\var{int})}$+$\\frac{R}{(1+\\var{int})^2}$+$\\frac{R}{(1+\\var{int})^3}$

$\\var{P}=R[\\frac{1}{(1+\\var{int})}$+$\\frac{1}{(1+\\var{int})^2}$+$\\frac{1}{(1+\\var{int})^3}]$

$\\var{P}=R[\\var{frac1}+\\var{frac2}+\\var{frac3}]$

$\\var{P} = R \\times \\var{num4}$

$\\frac{\\var{P}}{\\var{num4}}=R$

$\\var{R}=R$

Part (e)

The amount of interest paid is the difference between the amount borrowed ($P$) and the amount paid back (three payments of €$\\var{R}$)

Interest = $ 3 \\times \\var{R} - \\var{P}=\\var{Interest}$

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Which formula should we use to calculate how large each repayment will need to be?

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What is the value of $P$?

€[[0]]

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What is the value of $i$?

[[0]]

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What is the value of $n$?

[[0]]

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Calculate how large each repayment will need to be.

Please give your answer to the nearest cent.

€[[0]]

The formula for calculating the present value ($P$) of an annuity is:

$P=R\\left[\\frac{1-(1+i)^{-n}}{i}\\right]$

where $R$ represents the value of each repayment, $i$ represents the interest rate and $n$ represents the number of repayments.

Calculate the total amount of interest that the company will pay to the bank over the three years.

Please give your answer to the nearest cent.

€[[0]]

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A 1-year lease for a company car requires a payment of €280 at the end of each month. Find the present value of these payments if the annual interest rate is 7% compounded monthly.

", "licence": "None specified"}, "statement": "

A $\\var{years}$-year lease for a company car requires a payment of €$\\var{R}$ at the end of each month.

", "advice": "

The present value of an annuity, $P$ is given by:

$P=\\frac{R[1-(1+i)^{-n}]}{i}$

where $R$ represents the periodic payment, $i$ represents the interest rate per period and $n$ represents the number of payments.

$P$ represents the present value of the annuity, this is what we are asked to calculate.

$n$ represents the number of payments, there are 12 payments over $\\var{years}$ year(s) so $n$ is $12 \\times \\var{years}=\\var{n}$.

The value of each repayment, is €$\\var{R}$

Using the formula:

$P=\\frac{R[1-(1+i)^{-n}]}{i}$

$P=\\frac{\\var{R}[1-(1+\\var{int})^{-\\var{n}}]}{\\var{int}}$

$P=\\frac{\\var{R}[1-\\var{num}]}{\\var{int}}$

$P=\\frac{\\var{R}[\\var{num2}]}{\\var{int}}$

$P = \\var{R} \\times \\var{num3}$

$P=\\var{P}$

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Which formula should we use to calculate the present value of these payments?

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Find the present value of these payments if the annual interest rate is $\\var{perc}$% compounded monthly.

€[[0]]

The formula for calculating the present value ($P$) of an annuity is:

$P=R\\left[\\frac{1-(1+i)^{-n}}{i}\\right]$

where $R$ represents the value of each repayment, $i$ represents the interest rate and $n$ represents the number repayments.

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Find the present value of an amount where interest is compounded annually

", "licence": "None specified"}, "statement": "

The formula for calculating the present value of an investment is:

$P=\\frac{A}{(1+i)^n}$

$\\var{n}$ years from today, on his twenty-first birthday, Sean MacLeinn will receive a gift of €$\\var{A}$ from his great-aunt Priscilla. The annual rate of interest is $\\var{perc}$%.

", "advice": "

The present value formula is: $ P = \\frac{A}{(1+i)^n} $

Part (a)

A represents the principal sum invested , so in this example it is €$\\var{A}$.

Part (b)

i represents the rate of compound interest, in this example, the annual interest rate is $\\var{perc}$% so i is $\\frac {\\var{perc}} {100}=\\var{int}$.

Part (c)

n represents the number of compounding periods , so in this example it is $\\var{n}$ years.

Part(d)

Using the present value formula:

$ P = \\frac{A}{(1+i)^n} $

$ P = \\frac{\\var{A}}{(1+\\var{int})^\\var{n}} $

$ P = €\\var{P}$

What is the value of $A$?

€[[0]]

What is the value of $i$ written as a decimal?

€[[0]]

What is the value of $n$?

[[0]]

What is the present value of this gift? Please give your answer to the nearest cent.

€[[0]]

Interest rate does not match compounding period.

Find much money should be invested at $r$% per annum so that after $y$ years the amount will be £$A$, interest compounded daily.

", "licence": "Creative Commons Attribution 4.0 International"}, "statement": "

A sum of money is be invested with a nominal interest rate of $\\var{r}$% compounded daily so that after $\\var{yrs}$ years the amount will have grown to €$\\var{amt}$. You may assume that there are 365 days per annum.

The formula for calculating the present value of an investment is:

$P=\\frac{A}{(1+i)^n}$

", "advice": "

Part(a)

Interest is compounded daily for $\\var{yrs}$ years so there are a total of $365 \\times \\var{yrs} =\\var{n}$ compounding periods.

Part(b)

It is important to remember that the interest rate must match the compounding period.

The interest rate given in the question is ${\\var{r}}$% per annum.

The interest rate per day is $\\frac{\\var{r}}{365}=\\var{r/365}$%

Therefore $i=\\frac{\\var{r/365}}{100}=\\var{int}$

Part(c)

We want to find the present value of the amount $A=\\var{amt}$ due at the end of $n=\\var{yrs}\\times 365 = \\var{365*yrs}$ interest periods (days).

Hence the present value i.e. the amount to be invested is:
\\[ \\begin{eqnarray*} P&=&\\frac{A}{(1+i)^n}\\\\ \\\\ &=& \\frac{\\var{amt}}{(1+\\var{int})^{\\var{n}}}\\\\ \\\\ &=&\\var{p} \\end{eqnarray*} \\]

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What is the value of $n$?

[[0]]

What is the value of $i$?

[[0]]

Please give your answer to 8 decimal places.

What is the value of the sum of money initially invested?

€[[0]]

Please give your answer to two decimal places.

Calculate the final amount in a savings account where compound interest is earned annually

", "licence": "None specified"}, "statement": "

A lump sum of €$\\var{P}$ is deposited into a savings account, that pays compound interest at a rate of $\\var{perc}$% per annum for $\\var{n}$ years. If no withdrawals are made from the account, then the amount that the lump sum will have grown to is given by the formula:

$\\ A = P(1+i)^n $

", "advice": "

The compound interest formula is: $\\ A = P(1+i)^n $

Part (a)

P represents the principal sum invested , so in this example it is €$\\var{P}$.

Part (b)

i represents the rate of compound interest, in this example, the annual interest rate is $\\var{perc}$% so i is $\\frac {\\var{perc}} {100}=\\var{int}$.

Part (c)

n represents the number of compounding periods , so in this example it is $\\var{n}$ years.

Part(d)

The amount in the deposit account after $\\var{n}$ years is denoted by A. Using the compound interest formula:

$A=P(1+i)^n$

$A=\\var{P} \\times(1+\\var{int})^\\var{n}=\\var{A}$

What is the value of P?

€[[0]]

What is the value of i written as a decimal?

[[0]]

What is the value of n?

[[0]]

How much will be in the deposit account after $\\var{n}$ years? Please give your answer to the nearest cent.

€[[0]]

Calculate the annual interest rate for a savings account where A, P and n are given.

", "licence": "None specified"}, "statement": "

A lump sum of €$\\var{P}$ is deposited into a savings account that compounds interest annually for $\\var{n}$ years. If no withdrawals are made from the account, then the amount that the lump sum will have grown to is €$\\var{A}$.

The compound interest formula is:

$\\ A = P(1+i)^n $

", "advice": "

The compound interest formula is: $\\ A = P(1+i)^n $

Part (a)

P represents the principal sum invested , so in this example it is €$\\var{P}$.

Part (b)

A represents the amount in the deposit account after $\\var{n}$ years, so in this example it is €$\\var{A}$.

Part (c)

n represents the number of compounding periods , so in this example it is $\\var{n}$ years.

Part(d)

Using the compound interest formula:

$A=P(1+i)^n$

$\\var{A}=\\var{P}(1+i)^\\var{n}$

We need to rearrange the equation to find the value of $i$.

$\\frac{\\var{A}}{\\var{P}}=(1+i)^\\var{n}$

$\\var{ratio}=(1+i)^\\var{n}$

$\\sqrt[\\var{n}]{\\var{ratio}}=1+i$

$\\var{intplus}=1+i$

$i=\\var{int}$ so the annual interest rate is $\\var{perc}$%.

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What is the value of P?

€[[0]]

What is the value of A?

€[[0]]

What is the value of n?

[[0]]

What is the interest rate per annum?

Please give your answer as a percentage correct to two decimal places.

[[0]]%

Write your answer as a percentage.

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The compound interest formula is: $\\ A = P(1+i)^n $

Part (a)

n represents the number of compounding periods , so for Bank A it is $\\var{n1}$ years.

i represents the rate of compound interest, for Bank A, the annual interest rate is $\\var{perc1}$% so i is $\\frac {\\var{perc1}} {100}=\\var{int1}$.

The total amount saved after $\\var{n1}$ years is denoted by A. Using the compound interest formula:

$A=P(1+i)^n$

$A=\\var{P} \\times(1+\\var{int1})^\\var{n1}=\\var{A1}$

Part(b)

n represents the number of compounding periods. For Bank B, interest is compounded daily for $\\var{n1}$ years so there are a total of $365 \\times \\var{n1} =\\var{n2}$ compounding periods.

i represents the rate of compound interest. For Bank B, the interest rate is ${\\var{perc2}}$% per annum compounded monthly.

The interest rate per month is $\\frac{\\var{perc2}}{12}=\\var{int3}$%

Therefore $i=\\frac{\\var{int3}}{100}=\\var{int2}$

The amount saved after $\\var{n1}$ years is denoted by A. Using the compound interest formula:

$A=P(1+i)^n$

$A=\\var{P} \\times(1+\\var{int2})^\\var{n2}=\\var{A2}$

", "rulesets": {}, "parts": [{"prompt": "

Suppose that the potential customer chooses Bank A.

What is the value of $n$?

[[0]]

What is the value of $i$?

[[1]]

What is the value of $A$? Please give your answer to the nearest cent.

€[[2]]

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Suppose that the potential customer chooses Bank B.

What is the value of $n$?

[[0]]

What is the value of $i$? Please include all the decimal places in your answer.

[[1]]

What is the value of $A$? Please give your answer to the nearest cent.

€[[2]]

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Two rival high street banks offer customers a new deposit account.

Bank A offers an account that earns interest at a rate of $\\var{perc1}$% per annum where interest is compounded annually.

Bank B offers an account that earns interest at a rate of $\\var{perc2}$% per annum where interest is compounded daily.

Suppose that a potential customer has €$\\var{P}$ to invest for $\\var{n1}$ years.

The compound interest formula is:

$\\ A = P(1+i)^n $

You may assume that there are 365 days per annum.

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Compare two savings accounts with different interest rates.

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