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In order to obtain the NPV, you must first change the nominal rate per annum payable monthly/weekly/yearly/continuously into an effective rate per month.

{interest}% per annum payable monthly

As $i^{(12)}$={interest}%, divide this by 12 to obtain $i_{[p]}$ as $i_{[p]}={i^{(p)} \\over p}$ so then the interest rate payable per month is $i_{[12]}$={int}*$1 \\over 12$.

{interest}% per annum payable weekly

As we assume that each month has 4 weeks then we use:

$1+i=(1+{i^{(p)} \\over p})^p$

(see Numbas- Nominal Rates)

with:

$p$= 4
$i^{(p)}$= {intm}

In this case, $i$={intw}

{interest}% per annum payable daily

As we assume that each month has 30 days then we use:

$1+i=(1+{i^{(p)} \\over p})^p$

(see Numbas- Nominal Rates)

with:

$p$= 30
$i^{(p)}$= {intm}

In this case, $i$= {intd}

Force of interest corresponds to a nominal rate of {interest}% per annum

The force of interest $\\delta$ is the nominal rate payable continuously.

$(1+{i^{(p)} \\over p})^p=e^\\delta$ and so $i_{[p]}=e^{\\delta \\over p}-1$

(see Force of Interest)

with:

$p$= 12
$\\delta$= {interest}%

In this case, $i_{[12]}$= {force}

NPV

In order to work out the NPV, you must discount each value to time $t=0$:

$NPV=x_1v+x_2v^2+...+x_nv^n$

(see Numbas- Net Present Value)

In this case we have:

$NPV=-x_1-x_2v^1-x_2v^2...-x_2v^{n-2}+x_3v^n$

where:

$x_1$=£{value1} paid at $t=0$
$x_2$=£{value2} paid at $t=1,.....,t=n-2$
$x_3$=£{value3} received at $t=n$
n= 12*{n}

Substituting in the interest rates obtained above into the NPV expression gives the NPV if the nominal rate is {interest}% payable monthly/weekly/daily/continuously.

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

the nominal interest rate payable monthly is {interest}%?

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You have not given your answer to two decimal places.

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the nominal interest rate payable weekly {interest}%? (Assume each month has 4 weeks)

", "precisionMessage": "

You have not given your answer to two decimal places.

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the nominal interest rate payable daily is {interest}%? (Assume each month has 30 days)

", "precisionMessage": "

You have not given your answer to two decimal places.

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the force of interest, $\\delta$, corresponds to a nominal interest rate of {interest}% per annum?

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You have not given your answer to two decimal places.

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At time t=0 a construction company pays £{value1} to purchase a plot of land and materials to build a house. The comapny hires some workers that are paid a total of £{value2} at the end of each month for {m} months. The company sells the house at the end of year {n} for £{value3}.

Construct an Excel spreadsheet that shows the cashflow of each month and which analytically calculates the net present value at different interest rates.

What is the NPV (to two decimal places) if:

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