Question

After careful comparison shopping, Isabella Green decides to buy a new Toyota Camry. With some options added, the car has a price of $30,000 - including plates and taxes. Because she can't afford to pay cash for the car, she will use some savings and her old car as a trade-in to put down $8,500. She plans to finance the rest with a $21,500, 48-month loan at a simple interest rate of 9 percent.

What will her monthly payments be? Round the answer to the nearest cent.

$ ________per month

How much total interest will Isabella pay in the first year of the loan? Round the answer to the nearest cent.

$ _________

How much interest will Isabella pay over the full (48-month) life of the loan? Round the answer to the nearest cent.

$ __________

What is the APR on this loan? Round the answer to 1 decimal place.

___________%

Answer 1

Sol:

Given details,

Finance amount (P) = $ 21,500

Tenure of Loan (N) = 48 Months i.e 4 Years

Rate of interest (R) = 9% Per Annum i.e 9/12 = 0.75% or (0.0075) per month

Interest is Simple interest P.A.

i) Monthly Payment is

EMI calculation = [P x R x (1+R) ^n] / [(1+R)^ n-1]

= [$ 21500 x 0.0075] x (1+0.0075)⁴⁸ / (1+0.0075)⁴⁸ -1

= $ 161.25 x 1.4314 / (1.4314 -1 )

= $ 161.25 x 3.3180

= $ 535 ( rounded off 535.03) is Monthly payment.

ii)

Bifurcation of Interest and Principal :

Month 1 :

Loan amount $ 21500

Interest for 1st Month = $21500 x 0.0075

= $ 161 ( Round off 161.25 )

Principal for 1st Month = $ 535 - $ 161

= $ 374

Out standing loan amount at end of 1st month = $21500 - $ 374

= $ 21126

Note : Repeat the same calculation for next 11 months

Here I am giving a table for all the 11 months calculation.

Breakup of EMI payment of 1st Year Amount in $

Month	Pricipal (A)	Interest (B)	Monthly Payment (A+B)	Balance Loan
1	374	161	535	21126
2	377	158	535	20750
3	379	156	535	20370
4	382	153	535	19988
5	385	150	535	19603
6	388	147	535	19215
7	391	144	535	18824
8	394	141	535	18430
9	397	138	535	18033
10	400	135	535	17634
11	403	132	535	17231
12	406	129	535	16825
Total	4676	1744	6420

For the 1st year of loan Isabella have to pay $ 1744 .

iii)

Note: Here i am providing full table calculated answer

Month	Pricipal (A)	Interest (B)	Monthly Payment (A+B)	Balance Loan
1	374	161	535	21126
2	377	158	535	20750
3	379	156	535	20370
4	382	153	535	19988
5	385	150	535	19603
6	388	147	535	19215
7	391	144	535	18824
8	394	141	535	18430
9	397	138	535	18033
10	400	135	535	17634
11	403	132	535	17231
12	406	129	535	16825
Total	4676	1744	6420
13	409	126	535	16416
14	412	123	535	16004
15	415	120	535	15589
16	418	117	535	15171
17	421	114	535	14750
18	424	111	535	14325
19	428	107	535	13898
20	431	104	535	13467
21	434	101	535	13033
22	437	98	535	12596
23	441	94	535	12155
24	444	91	535	11711
Total	5114	1306	6420
25	447	88	535	11264
26	451	84	535	10814
27	454	81	535	10360
28	457	78	535	9902
29	461	74	535	9442
30	464	71	535	8977
31	468	67	535	8510
32	471	64	535	8038
33	475	60	535	7564
34	478	57	535	7085
35	482	53	535	6604
36	486	50	535	6118
Total	5594	827	6420
37	489	46	535	5629
38	493	42	535	5136
39	497	39	535	4640
40	500	35	535	4139
41	504	31	535	3635
42	508	27	535	3128
43	512	23	535	2616
44	515	20	535	2101
45	519	16	535	1581
46	523	12	535	1058
47	527	8	535	531
48	531	4	535	0
Total	6118	303	6420

Total Interest for 4 years is 1744+1306+827+303 = $ 4180 (Rounded off)

iv)

APR on this Loan

APR = [(Interest/Principal/n​​)×365]×100

where:

Interest=Total interest paid over life of the loan

Principal=Loan amount

n=Number of days in loan term​

APR = [4180 / 21500 /4*365] *365 *100

= 0.00013316 x 365 x 100

APR = 4.86 %

Assume 365 days in a year for all 4 years of Loan period.

___________________________***THE END***__________________________