Question

Can you help to answer this question step by step? The answer is 10857.27.

Problem 41.21 | Betty borrows 19,800 from Bank X. Betty repays the loan by making 36 equal payments of principal at the end of each month. She also pays interest on the unpaid balance each month at a nominal rate of 12%, compounded monthly. Immediately after the 16th payment is made, Bank X sells the rights to future payments to Bank Y. Bank Y wishes to yield a nominal rate of 14%, compounded semi-annually, on its investment. What price does Bank X receive?

Answer 1

GIVEN DATA FROM THE PROBLEM

BETTY BORROWS 19,800 FROM BANK X AND REPAYS LOAN BY MAKING 36 EQUAL PAYEMENTS

NOMINAL RATE = 12% OF X

NOMINAL RATE =14% OF Y

BELOW TABLE SHOWS THAT PRICE DOES BANK X RECIEVE

Month	Opening	Payment	Principle	Interest	Closing
1	$19,800	$748.00	$550.00	$198	$19,250
2	$19,250	$742.50	$550.00	$193	$18,700
3	$18,700	$737.00	$550.00	$187	$18,150
4	$18,150	$731.50	$550.00	$182	$17,600
5	$17,600	$726.00	$550.00	$176	$17,050
6	$17,050	$720.50	$550.00	$171	$16,500
7	$16,500	$715.00	$550.00	$165	$15,950
8	$15,950	$709.50	$550.00	$160	$15,400
9	$15,400	$704.00	$550.00	$154	$14,850
10	$14,850	$698.50	$550.00	$149	$14,300
11	$14,300	$693.00	$550.00	$143	$13,750
12	$13,750	$687.50	$550.00	$138	$13,200
13	$13,200	$682.00	$550.00	$132	$12,650
14	$12,650	$676.50	$550.00	$127	$12,100
15	$12,100	$671.00	$550.00	$121	$11,550
16	$11,550	$665.50	$550.00	$116	$11,000
17	$11,000	$660.00	$550.00	$110	$10,450
18	$10,450	$654.50	$550.00	$105	$9,900
19	$9,900	$649.00	$550.00	$99	$9,350
20	$9,350	$643.50	$550.00	$94	$8,800
21	$8,800	$638.00	$550.00	$88	$8,250
22	$8,250	$632.50	$550.00	$83	$7,700
23	$7,700	$627.00	$550.00	$77	$7,150
24	$7,150	$621.50	$550.00	$72	$6,600
25	$6,600	$616.00	$550.00	$66	$6,050
26	$6,050	$610.50	$550.00	$61	$5,500
27	$5,500	$605.00	$550.00	$55	$4,950
28	$4,950	$599.50	$550.00	$50	$4,400
29	$4,400	$594.00	$550.00	$44	$3,850
30	$3,850	$588.50	$550.00	$39	$3,300
31	$3,300	$583.00	$550.00	$33	$2,750
32	$2,750	$577.50	$550.00	$28	$2,200
33	$2,200	$572.00	$550.00	$22	$1,650
34	$1,650	$566.50	$550.00	$17	$1,100
35	$1,100	$561.00	$550.00	$11	$550
36	$550	$555.50	$550.00	$6	$0

Payment amounts from Month 17 to Month 36 (20 months) totals to $12,155. 14% compounded monthly is 1.1340% per month. Hence using the excel function =NPV(1.1340%,660.00,654.50,649.00,643.50,638.00,632.50,627.00,621.50,616.00,610.50,605.00,599.50,594.00,588.50,583.00,577.50,572.00,566.50,561.00,555.50), we get the answer $10,857. Answer is basically the present value of cash flows the Bank Y will get from Month 17 to Mon 36.