Question

Question 3

Chloe Colburn purchased home appliances for her new apartment. Store allowed her to defer payments (interest is still being charged even though payments are deferred) for six months and to make 36 equal end-of-month payments thereafter. The original note was for $15,000, with interest at 9% per annum compounded monthly. After 26 monthly payments, Chloe considers getting a loan from the bank to pay her debts in one lump sum. She would pay the bank $186 per month for the next 30 months.

1. a) Find the original monthly payment made to the store.
2. b) Find the lump-sum payoff amount she needs to take loan from the bank.
3. c) What monthly rate of interest is the bank charging on this loan???

Answer 1

	Original note(P)	$15,000
	number of payments(n)	36
	annual rate of interest( R)	9%		0.09000
	monthly rate of interest( r)	0.75%	=9%/12	0.00750
a)	Orinial monthly payment	=P*r*(1+r)^n/((1+r)^n-1)
		=15000*0.0075*1.0075^36/(1.0075^36-1)
	Orinial monthly payment(M)	477.00
b)	Balance loan amount after 26 monthly payments
Month	Opening balance	Interest	Payment	Closing balance
1	15000	112.5	(477.00)	14,635.50
2	14,635.50	109.76628	(477.00)	14,268.27
3	14,268.27	107.012057	(477.00)	13,898.29
4	13,898.29	104.237178	(477.00)	13,525.53
5	13,525.53	101.441487	(477.00)	13,149.98
6	13,149.98	98.6248279	(477.00)	12,771.61
7	12,771.61	95.7870442	(477.00)	12,390.40
8	12,390.40	92.9279771	(477.00)	12,006.33
9	12,006.33	90.047467	(477.00)	11,619.38
10	11,619.38	87.1453531	(477.00)	11,229.53
11	11,229.53	84.2214733	(477.00)	10,836.76
12	10,836.76	81.2756644	(477.00)	10,441.03
13	10,441.03	78.307762	(477.00)	10,042.35
14	10,042.35	75.3176003	(477.00)	9,640.67
15	9,640.67	72.3050123	(477.00)	9,235.98
16	9,235.98	69.26983	(477.00)	8,828.25
17	8,828.25	66.2118838	(477.00)	8,417.47
18	8,417.47	63.131003	(477.00)	8,003.60
19	8,003.60	60.0270156	(477.00)	7,586.63
20	7,586.63	56.8997483	(477.00)	7,166.54
21	7,166.54	53.7490265	(477.00)	6,743.29
22	6,743.29	50.5746743	(477.00)	6,316.87
23	6,316.87	47.3765144	(477.00)	5,887.25
24	5,887.25	44.1543683	(477.00)	5,454.41
25	5,454.41	40.9080562	(477.00)	5,018.32
26	5,018.32	37.6373967	(477.00)	4,578.96
	Thus, lump sum loan amount	4,578.96
c)	Monthly rate of interest on new loan(R1)
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