Question

If you borrow $20,000, you have to repay in equal instalments over four years. Interest Rate is 9%. What is the interest payment in the fourth year, 14.

a) 1499 b)1171 c)510 d)977 e)1406 f)814

Answer 1

c) 510

You can spreadsheet here with the formula =ipmt(rate, period, no. of periods, present value)

=IPMT(9%,4,4,20000)

Rate is the rate of interest

The period is the period we are talking about i.e 4th

the answer is 510.

If we want to solve it by hand we will first derive EMI using the following formula

[P x R x (1+R)^N]/[(1+R)^N-1]

It can be used for calculating monthly and yearly installments with changes.

Here

((20000×9%)(1+9%)^4)÷((1+9%)^4−1)

=6173.37

So this is what we will give as installments per year, Now in this amount both the interest and principal are included.

For 1 year, at 9% interest rate, interest will be 1800, so here 1800 is for interest, and rest 4373.37 goes towards the principal. For the next year (20,000-4373.37) is remaining and the interest will be charged on that amount. 15,626.63 is the remaining amount for the next year and interest on it will be 1406.4. and so on

Let's look at it in table format

Year	EMI	Interest	Principal
1	$6,173.37	1,800	$4,373.37
2	$6,173.37	1,406	$4,766.98
3	$6,173.37	977	$5,196.00
4	$6,173.37	510	$5,663.65
Total	24693	4693	20000

You can see that in the 4th year, interest is 510.