Question

Joan borrowed

​$15,000.00

to buy a car. She repaid

​$4000.00

four

months later and

​$6800.00

eight

months later. After twelve​ months, she borrowed an additional

​$4800.00​,

and repaid

​$4400.00

after

19

months. She paid the entire​ balance, including the​ interest, after 24 months. Interest was

6​%

compounded monthly for the first year and

5.5​%

compounded monthly for the remaining time. What was the size of the final​ payment?

Answer 1

First of all let us find out the monthly interest rate during the year-1 and later on

Given the interest rate on Year-1 is 6%

Since it is given that it is compounded monthly hence

For year -1

(1+X)¹² = 1.06

Hence X = 0.486755%

For Year -2

(1+X)¹² = 1.055

X = 0.44717%

Month	Opening Borrowed Amount	Interest Amount	Repaid Amount	Additional Amount Borrowed	Closing Loan Balance
1	15,000.00	73.01	-	-	15,073.01
2	15,073.01	73.37	-	-	15,146.38
3	15,146.38	73.73	-	-	15,220.11
4	15,220.11	74.08	4,000.00	-	11,294.19
5	11,294.19	54.98	-	-	11,349.17
6	11,349.17	55.24	-	-	11,404.41
7	11,404.41	55.51	-	-	11,459.92
8	11,459.92	55.78	6,800.00	-	4,715.70
9	4,715.70	22.95	-	-	4,738.66
10	4,738.66	23.07	-	-	4,761.72
11	4,761.72	23.18	-	-	4,784.90
12	4,784.90	23.29	-	4,800.00	9,608.19
13	9,608.19	42.96	-	-	9,651.16
14	9,651.16	43.16	-	-	9,694.31
15	9,694.31	43.35	-	-	9,737.66
16	9,737.66	43.54	-	-	9,781.21
17	9,781.21	43.74	-	-	9,824.95
18	9,824.95	43.93	-	-	9,868.88
19	9,868.88	44.13	4,400.00	-	5,513.01
20	5,513.01	24.65	-	-	5,537.66
21	5,537.66	24.76	-	-	5,562.43
22	5,562.43	24.87	-	-	5,587.30
23	5,587.30	24.98	-	-	5,612.28
24	5,612.28	25.10	-	-	5,637.38

Hence the amount of loan of final payment will be 5637.32

Please note that interest is calculated using the opening balance at the rate we found out above for year -1 and there after.