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Sample of Finance Homework Illustrations and Solutions:

Illustration: 1 Finance company makes an offer to deposit a sum of $ 1,100 and then

receive a return of $ 2,500 p.a. indefinitely and the rate of interest is 12% p.a.

Solution :

In this case, a person should accept the offer only if the PV of the perpetuity is more

than the initial deposit of $1,100.

If the rate of interest is 8%, then using the Equation

𝑃𝑉𝑝 = Annual Cash flow/r

= $. 80/.08

= $1,000.

If the rate of interest is 5% then

𝑃𝑉𝑝 = Annual Cash flow/r

=$ 80/0.5

= $ 1,600.

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Illustration: 2 In setting up an educational fund, a person agrees to make five

annual-payments of $ 5,000 each into a ‘college fund programme’. The first payment is

to made 12 years from now and the ‘college fund programme’ wishes that upon making

the last payment, the amount available should have grown to $ 30,000. What should be

the minimum rate of return on this fund ?

Solution :

In this case, the amount of $ 30,000 can be considered as the future value of the

annuity of $5,000. Consider the Equation . IB to find out the future value of the

annuity:

FV = Annuity Amount × CVA𝐹(𝑟 ,𝑛)

$30,000 = $5,000 × 𝐶𝑉𝐴𝐹(𝑟,𝑛)

6 = 𝐶𝑉𝐴𝐹(𝑟 ,𝑛)

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Now, looking at the 5 year row in Table , the value 6 falls between the table value of

5.985 and 6.105 in the 9% column and 10% column respectively. Hence, the rate of

return on this annuity is slightly higher than 9% So, the college fund programme must

earn a rate of return of slightly higher than 9% on the annual deposit to accumulate a

target amount of $ 30,000, In this case, the fact that the annuity starts from r12 year

from now is irrelevant in computing the interest rate because the annuity table

compounds only during the interval period over which the annuity payments are being

made.

Finding out the number of periods : Something, one may be interested to find out

the time over which a certain amount will grow at a given rate of interest to a certain

value. In this case, the value of ‘n’, can be ascertained by solving Equation .

FV = PV (1 + 𝒓)𝒂

Illustration: 3 $1,000 is deposited into an interest-bearing account that pays 10%

interest compounded yearly. The investor’s goal is $ 1,500. How many years must the

principal earn compound interest before the desired amount is realized ?

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Solution :

This situation can be visualized as to what is the period over which the amount or $

1,000 will cumulate to $1,500 at 10% rate of interest.

Substituting the values in to Equation .

FV = PV(1 + 𝒓)𝒏

$ 1,500 = $1,000 (1 + . 10)𝑛

$1,500 / $ 1,000 = (1 + . 10)𝑛

1.5 = (1 + . 10)𝑛

Now, look up the 10% column in Table and read vertically until a value that equals or

approximates the computed value of 1.5 is found. This is 1.611, which corresponds to 5

years. If $ 1,000 principal is left at 10% interest for 5 years. the resulting compound

amount will be $ 1,611, This exceeds the desired $ 1,464 The investor should leave the

deposit for the entire fifth year because of the assumption of compounding only at the

end of each years, and he will then receive an amount of $ 1,611.

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Illustration: 4 A machine costs $ 98.000 and its effective life is estimated at 12 years.

If the scrap value is $ 3,000, what should be retained out of profit at the end of each

year to accumulate at compound interest rate at 5% p.a., so that a new machine can be

purchased after 12 years ?

Solution :

Effective cost of the machine = $98,000 – 3,000 = $95,000.

Now FV = Annuity Amount × 𝐶𝑉𝐴𝐹(5% 12𝑦)

or $95,000 = $95,000 – 15.917

= $968

So, annual profit retained of $ 5,968 for 12 years @ 5% will accumulate to $ 95,000

which together with scrap value of $ 3000 can be used to purchase the new machine.