Question

a 30 year loan of 1000 is repaid with payments at the end of each year. Each of the first 10 payments equals the amount of interest due. Each of the next 10 payments equals 150% of the amount of interest due. Each of the last 10 payments is X. The lender charges interest at an effective annual rate of 10%. Calculate X.

please explain, having much trouble with this problem, Thanks!

Answer 1

For first 10 years the loan principal for not paid only interest was paid hence outstanding balance of loan is $ 1000 (because interest = payment).

For next 10 years the loan principal balance:

Years	Principal at beginning of the years = Outstanding Principal - Payment	Interest = 10% of Principal at beginning	Principal paid	Payment = 150%*Interest	Outstanding Principal
11	1,000.00	100.00	50.00	150.00	950.00
12	950.00	95.00	47.50	142.50	902.50
13	902.50	90.25	45.13	135.38	857.38
14	857.38	85.74	42.87	128.61	814.51
15	814.51	81.45	40.73	122.18	773.78
16	773.78	77.38	38.69	116.07	735.09
17	735.09	73.51	36.75	110.26	698.34
18	698.34	69.83	34.92	104.75	663.42
19	663.42	66.34	33.17	99.51	630.25
20	630.25	63.02	31.51	94.54	598.74

Loan balance at 20^th year end = 598.74

Finding payment per period:
P = Loan balance =	$598.74
R = Rate =	10.000000%
N = Numbers of payment = Balance 10 years =	10
PMT = Payment = P x R x (1+R)^N / ((1+R)^N - 1) = X =	97.44

Formula for calculating payment (working)

PMT = P x R x (1+R)^N / ((1+R)^N - 1)

PMT = 598.74*10%*(1+10%)^10/((1+10%)^10-1)

PMT = $97.44 (Rounding to nearest cent or two decimal places)

Payment or X = $ 97.44

Years	Principal at beginning of the years	Interest	Principal paid	Payment	Outstanding Principal
21	598.74	59.87	37.57	97.44	561.17
22	561.17	56.12	41.32	97.44	519.85
23	519.85	51.98	45.46	97.44	474.39
24	474.39	47.44	50.00	97.44	424.39
25	424.39	42.44	55.00	97.44	369.39
26	369.39	36.94	60.50	97.44	308.89
27	308.89	30.89	66.55	97.44	242.34
28	242.34	24.23	73.21	97.44	169.13
29	169.13	16.91	80.53	97.44	88.61
30	88.61	8.86	88.58	97.44	0.03