Question

Mr Smith is struggling to repay his loan of K200,000 with payments of K4,279 made monthly in arrears for 5 years. (i) Find the amount of the level annual repayment. (ii) Hence, otherwise, calculate the APR of Mr Smiths loan, After exactly one year, a loan company oers to `help' Mr Smith by restructuring his loan with new monthly payments of K2,744.90 made in arrears. (iii) Assuming the company charges the same APR as Mr Smiths original loan, calculate the term of the new loan. (iv) Calculate how much more interest in total Mr Banda will pay on his restruc- tured loan than on his original loan.

Answer 1

Tenure of loan =5*12=60 month

So, for the first loan

So, monthly interest rate is 0.858%. Level Payment Annual=4279*12= K51348.

ii) APR of the Loan=(1+858%)^12-1=10.80%

Below is the amortization schedule:

Month	Principal	Interest	Payment	Outstanding Principal
0	200000	0	0	200000
1	200000	1716.681	-4279	197437.6809
2	197437.7	1694.687	-4279	194853.3684
3	194853.4	1672.505	-4279	192246.8737
4	192246.9	1650.133	-4279	189618.0064
5	189618	1627.568	-4279	186966.5745
6	186966.6	1604.81	-4279	184292.3842
7	184292.4	1581.856	-4279	181595.2403
8	181595.2	1558.705	-4279	178874.9457
9	178874.9	1535.356	-4279	176131.3017
10	176131.3	1511.806	-4279	173364.1079
11	173364.1	1488.054	-4279	170573.1622
12	170573.2	1464.098	-4279	167758.2607

iii) For his new loan, principal=167758.26, rate=0.858%/month,PMT=2744.9

So, the tenure of the new loan is 87 months or 7 year 3 month

iv) For the first case he would paid interest of=(4279*60)-200000= K56740

For the second case he would pay interest= (2744.90*87)-167758.3=K71048

So, he will pay more interest on his second loan=(71048-56740)=K14308