Question

A loan of Kenya Shs 5,000,000/= disbursed today is repaid in four installments commencing at the end of year one. The second repayment is at the end of year two and is half as much again as the first installment and is 15% less than the third installment (due at the end of year four). The final installment is due at the end of year five and is 25% more than the first installment.

The rate of interest is 14% per annum in years one and two; 15% per annum in years three and four; and 11% per annum in years, five and six. Compute the amount of each installment.

Answer 1

Let the loan amount paid at the end of year 1 be "x". Thus second repayment amount = x/2. Also 2nd repayment is 15% less than the 3rd repayment. Thus 3rd repayment - 0.15*3rd repayment = 2nd repayment

or 0.85*3rd repayment = x/2

or 3rd repayment = x/(2*0.85)

Thus 3rd repayment = x/1.70

4th repayment = 1.25x

Thus putting the above values in the loan amortization table we get the following:

Year	Loan amount due at the beginning of the period	Amount paid during the year	Interest rate (%)	Interest amount	Principal amount paid	Loan amount due at the end of the period
1	5,000,000.00	2,212,986.47	14.00	700,000.00	1,512,986.47	3,487,013.53
2	3,487,013.53	1,106,493.24	14.00	488,181.89	618,311.34	2,868,702.18
3	2,868,702.18	0.00	15.00	430,305.33	0.00	3,299,007.51
4	3,299,007.51	1,301,756.75	15.00	494,851.13	806,905.62	2,492,101.89
5	2,492,101.89	2,766,233.09	11.00	274,131.21	2,492,101.89	0.00

Thus 1st installment = $2,212,986.47

2nd installment = 1,106,493.24

3rd installment = 1,301,756.75

4th installment = 2,766,233.09