Question

A loan of $5000 is repaid with annual payments at the end of each year of $1200,$800,$1300 and X. Assume the loan has 10% effective interest per year. a) Determine X b) Determine the amount of interest paid with the third payment.

Answer 1

Loan amortisation schedule
Year	Annual pmts.	Tow. Int. at 10% on O/s loan bal.	Tow. Loan	Loan bal.
1	2	3=Prev. 5*10%	4=2-3	5=Prev. 5-Current 4
0				5000
1	1200	500	700	4300
2	800	430	370	3930
3	1300	393	907	3023
4	3325.3	302.3	3023	0
Total	6625.3	1625.3	5000

The present value of the loan= 5000

as the effective interest is given as 10%

with every annual pmt. We need to subtract the interest on the o/s bal. of the loan

to see how much of the loan is repaid

Now, subtract that princpal paid from the previous loan bal. --we get the principal o/s at start of next yr.

Like, this we need to calculate till end of 3rd year ---to find X

to do that, it is better to draw up a loan amortisation schedule/Table , as above

to determine the answer fo the questions.

So, reading from the above amortisation table,

a) X= $ 3325.3

&

b) The amount of interest paid with the third payment= $ 393 ( 3930*10%)