Interest
1 Introduction
The purpose of this chapter and the next chapter is to consider a key area for management accountants – the appraisal of capital investments.
In this chapter we will look at interest on capital and continue in the next chapter with the use of these techniques in investment appraisal.
2 Simple interest
A sum of money invested or borrowed is known as the principal.
When money is invested it earns interest; similarly when money is borrowed, interest is payable.
With simple interest, the interest is receivable or payable each year, but is not added to the principal.
A man invests $200 on 1 January each year. On 31 December each year simple interest is credited at 15% but this interest is put in a separate account and does not itself earn interest.
Find the total amount standing to his credit on 31 December following his fourth payment of $200.
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3 Compound interest
With compound interest the interest is added each year to the principal and in the following year the interest is calculated on the total.
A man invests $500 now for 3 years with interest at 10% p.a.
How much will be in his account after 3 years?
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The amount (A) at the end of the n’th year is given by:
This is also known as the future value (or terminal value)
A man invests $800 at 6%p.a. for 5 years.
How much will be in his account at the end of 5 years?
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4 Effective Rate
For simplicity, the previous compound interest examples have assumed that interest is calculated only once a year.
However in practice interest may be calculated on a monthly or even daily basis. The same formula can still be used, but we need to distinguish between the nominal and annual percentage rates.
There are usually two rates quoted by financial institutions. The first is the nominal rate and the other, the rate actually earned, is known as the effective or the annual percentage rate (APR).
A credit card company charges a nominal rate of 2% per month.
If a customer has purchased $100 worth of goods on his credit, calculate the amount she will owe after one year, and also the annual percentage rate (APR)
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5 Discounting
In the previous example we calculated the future value of cash flows by adding on (or compounding) the interest.
We can do the same exercise in reverse to calculate the amount now that is equivalent to future flows, by removing interest.
This exercise is known as discounting and the equivalent amount is known as the present value.
What amount now is equivalent to $800 in 4 years time, with interest at 10% p.a.?
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The formula for this is
However tables are provided in the examination which give the discount factors
at different rates of interest for different numbers of years.
What is the present value of 1,200 receivables in 12 years time, with interest at 13%?
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6 Annuities
An annuity is regular payment of the same amount each year.
The present value of an annuity is given by the formula:
but again, tables are provided for this in the examination.
Interest rate is 12% p.a.
What is the present value of $500 receivable in 1 years time and thereafter every year for a total of 8 receipts?
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A man expects to receive $1,000 in each of 9 years, with the first receipt being in 4 years time.
What is the present value of the receipts if interest is 8% p.a.?
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7 Perpetuities
Perpetuity is an annuity that is expected to continue for an indefinitely long period of time.
The present value of a perpetuity is given by the formula:
Interest rate is 12% p.a.
What is the present value of $5,000 receivable in 1 years time and thereafter in perpetuity?
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Interest
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