Question

Ralph has just borrowed $1380 to purchase a new stereo, at a nominal rate of interest of 11% convertible monthly. Although he is charged interest from the moment he borrows the money, the first payment is not due for 11 months. If he will make 24 monthly payments, how much interest is in the 17th payment?

Answer 1

It is given that $ 1380 is borrowed and interest chargeable immediately. However, it is not paid for 11 months. As such, interest charged for every month upto 11 months, is added to the outstanding principal amount and interest for the next month is calculated on the opening principal amount.

At the end of the 11^th month, total principal outstanding is $ 1,525.71 (including accumulated interest for 11 months). This amount is repaid over 24 equal monthly instalments along with interest for each month.

Please find the below table computed for calculating principal and interest due for each month:

Month	Opening Principal ($)	Interest @ 11% p.a. on opening principal ($)	Payment of Principal ($)	Payment of interest ($)	Closing principal + Interest (if unpaid) ($)
0	1,380.00	-	-	-	-
1	1,380.00	12.65	-	-	1,392.65
2	1,392.65	12.77	-	-	1,405.42
3	1,405.42	12.88	-	-	1,418.30
4	1,418.30	13.00	-	-	1,431.30
5	1,431.30	13.12	-	-	1,444.42
6	1,444.42	13.24	-	-	1,457.66
7	1,457.66	13.36	-	-	1,471.02
8	1,471.02	13.48	-	-	1,484.51
9	1,484.51	13.61	-	-	1,498.12
10	1,498.12	13.73	-	-	1,511.85
11	1,511.85	13.86	-	-	1,525.71
12	1,525.71	13.99	63.57	13.99	1,462.14
13	1,462.14	13.40	63.57	13.40	1,398.56
14	1,398.56	12.82	63.57	12.82	1,334.99
15	1,334.99	12.24	63.57	12.24	1,271.42
16	1,271.42	11.65	63.57	11.65	1,207.85
17	1,207.85	11.07	63.57	11.07	1,144.28
18	1,144.28	10.49	63.57	10.49	1,080.71
19	1,080.71	9.91	63.57	9.91	1,017.14
20	1,017.14	9.32	63.57	9.32	953.57
21	953.57	8.74	63.57	8.74	890.00
22	890.00	8.16	63.57	8.16	826.42
23	826.42	7.58	63.57	7.58	762.85
24	762.85	6.99	63.57	6.99	699.28
25	699.28	6.41	63.57	6.41	635.71
26	635.71	5.83	63.57	5.83	572.14
27	572.14	5.24	63.57	5.24	508.57
28	508.57	4.66	63.57	4.66	445.00	68.23	17th payment
29	445.00	4.08	63.57	4.08	381.43
30	381.43	3.50	63.57	3.50	317.86
31	317.86	2.91	63.57	2.91	254.28
32	254.28	2.33	63.57	2.33	190.71
33	190.71	1.75	63.57	1.75	127.14
34	127.14	1.17	63.57	1.17	63.57
35	63.57	0.58	63.57	0.58	(0.00)

The 17^th month of payment is highlighted above. Total payment made in the 17^th month is $ 68.23, of which $ 63.57 is principal and $ 4.66 is interest.