Question

Nicola borrows a $24000 loan from Steve. She agrees to pay interest on the loan at the end of each year for 8 years, and will repay the capital by accumulation of a sinking fund. The sinking fund deposits are such that the net amount of the loan decreases linearly, resulting in a level repayment of principal at the end of each year. The interest rate on the loan is 5% over the first 4 years and 4.5% over the next 4 years. The sinking fund earns a fixed 4% interest rate per annum.

(a) Find the total amount of the 5th installment paid by Nicola. (Ans. $3600)

(b) Compare this with the case when Nicola repays the loan with 8 equal annual installments.

Answer 1

Principle amount repayment/year will be=24000/8=3000/yr

Year	Amount o/s	Interest(5%/4.5%	Total	Repayment amount	Balance
1	24000	1200	25200	4200	21000
2	21000	1050	22050	4050	18000
3	18000	900	18900	3900	15000
4	15000	750	15750	3750	12000
5	12000	540	12540	3540	9000
6	9000	405	9405	3405	6000
7	6000	270	6270	3270	3000
8	3000	135	3135	3135	0
Total				29250

b) when Nicola repays the loan with 8 equal annual installments.=29250/8=3656.25/installment

Difference between two=3656.25-3540=116.25