Question

4. A debt of P200,000 is to be discharged by ten semi-annual payments, the first to be made 6 months after the loan is given. The debt will be discharged by 5 equal payments each P20,000 and by 5 other equal payments of such amount that the final payment will liquidate the debt. If interest is 12 % compounded semi-annually, what is the amount of the last 5 payments? Construct an amortization schedule indicating the following: Period, Principal at the beginning of period, Interest earned at 12 % compounded semi-annually, Payment at the end of period, and payment to the principal. Then indicate the totals per column.

Answer 1

12% p.a. compunded semi-annually = 6% for a period of 6 months

let the amount of last 5 payments be X

From the concept of Present Value

Present value of Loan = present value of installments at 12% p.a. compunded semi-annually

=> 200000 = (20000/1.06+ 20000/1.06²+...+20000/1.06⁵) + (X/1.06⁶+....+ X/1.06¹⁰)

=> 200000 = 18867.92+17799.93+....+14945.16+ X/1.06⁵ * (1/1.06+ 1/1.06² + ... + 1/1.06⁵)

=> 200000 = 84247.28 + X/1.06⁵ * 4.212364

=> X = 115752.72/4.212364*1.06⁵

= 36773.48

Hence the amount of other 5 payments is P36773.48 each

The amortization schedule is as given below :

Period	Principal at	Interest earned at	Payment at	payment to
	beginning of	12% compounded	end of period	principal
	period	semi-annually
1	200000	12000	20000	8000
2	192000	11520	20000	8480
3	183520	11011.2	20000	8988.8
4	174531.2	10471.87	20000	9528.128
5	165003.1	9900.184	20000	10099.82
6	154903.3	9294.195	36773.48	27479.28
7	127424	7645.439	36773.48	29128.04
8	98295.94	5897.756	36773.48	30875.72
9	67420.22	4045.213	36773.48	32728.26
10	34691.96	2081.518	36773.48	34691.96
11	0
	Total	83867.38	283867.4	200000