Question

Ian Borrows $5,600 at rate of interest i(2)=5.55%. He repays the loan by making N payments of $350 at the end of each half-year plus a final larger payment of X at the end of N+1 half-years.

Find X (nearest cent)

Answer 1

Calculating the Value of X(i.e., the last large final payment) using Amortization Scchedule:-

Half-Yearly	Beg bal.	Payment	Interest amount	Principal Amount	End Bal.
1	5,600.00	350.00	155.40	194.60	5,405.40
2	5,405.40	350.00	150.00	200.00	5,205.40
3	5,205.40	350.00	144.45	205.55	4,999.85
4	4,999.85	350.00	138.75	211.25	4,788.60
5	4,788.60	350.00	132.88	217.12	4,571.48
6	4,571.48	350.00	126.86	223.14	4,348.34
7	4,348.34	350.00	120.67	229.33	4,119.00
8	4,119.00	350.00	114.30	235.70	3,883.31
9	3,883.31	350.00	107.76	242.24	3,641.07
10	3,641.07	350.00	101.04	248.96	3,392.11
11	3,392.11	350.00	94.13	255.87	3,136.24
12	3,136.24	350.00	87.03	262.97	2,873.27
13	2,873.27	350.00	79.73	270.27	2,603.00
14	2,603.00	350.00	72.23	277.77	2,325.24
15	2,325.24	350.00	64.53	285.47	2,039.76
16	2,039.76	350.00	56.60	293.40	1,746.36
17	1,746.36	350.00	48.46	301.54	1,444.83
18	1,444.83	350.00	40.09	309.91	1,134.92
19	1,134.92	350.00	31.49	318.51	816.41
20	816.41	350.00	22.66	327.34	489.07
21	489.07	502.64	13.57	489.07	0.00

So, Final Large Payment of X is $502.64 ($489.07 + $13.57)

Note- The following Columns are calculated based on:

- Interest amount = beg. Balnace*Monthly interest rate

- Principal maount = Payment - Interest amount

- End Bal. = Beg. Bal + Interest - Payment

If you need any clarification, you can ask in comments.     

If you like my answer, then please up-vote as it will be motivating