Question

A loan of $100,000 is to be repaid by two equal repayments of X. One repayment is due at the end of 2 years, the second repayment is due at the end of 6 years. The interest rate is at 4% p.a. compounded quarterly for the first 3 years and then 4.4% p.a. compounded quarterly thereafter. What is the size of each repayment?

Select one:

a. $58,762.97

b. $58,222.14

c. $57,989.46

d. $56,779.19

Answer 1

Duration of the loan=6 years

No.of Repayments = X

Interest rate per Quarter during the first three years = 4% /4 = 1% per Quarter

Interest rate per Quarter during the next three years = 4.4% /4 = 1.1% per Quarter

Let the Amount of Repayment is $ 58762.97( By going with the verification of Options)

S.No	Opening Balance	Interest @ 1%	Total balance	Amount paid	Outstanding balance
1	$100,000	$1,000	$101,000	$0	$101,000
2	$101,000	$1,010	$102,010	$0	$102,010
3	$102,010	$1,020	$103,030	$0	$103,030
4	$103,030	$1,030	$104,060	$0	$104,060
5	$104,060	$1,041	$105,101	$0	$105,101
6	$105,101	$1,051	$106,152	$0	$106,152
7	$106,152	$1,062	$107,214	$0	$107,214
8	$107,214	$1,072	$108,286	$58,762.97	49522.70056
9	$49,523	$495	$50,018	$0	50017.92757
10	$50,018	$500	$50,518	$0	50518.10684
11	$50,518	$505	$51,023	$0	51023.28791
12	$51,023	$510	$51,534	$0	51533.52079

S.No	Opening Balance	Interest @ 1.1%	Total balance	Amount paid	Outstanding balance
13	51533.52079	566.8687287	52100.38952	0	52100.38952
14	52100.38952	573.1042847	52673.49381	0	52673.49381
15	52673.49381	579.4084319	53252.90224	0	53252.90224
16	53252.90224	585.7819246	53838.68416	0	53838.68416
17	53838.68416	592.2255258	54430.90969	0	54430.90969
18	54430.90969	598.7400066	55029.64969	0	55029.64969
19	55029.64969	605.3261466	55634.97584	0	55634.97584
20	55634.97584	611.9847342	56246.96057	0	56246.96057
21	56246.96057	618.7165663	56865.67714	0	56865.67714
22	56865.67714	625.5224486	57491.19959	0	57491.19959
23	57491.19959	632.4031955	58123.60279	0	58123.60279
24	58123.60279	639.3596306	58762.96242	$58,762.97	-0.007584201

Since the loan balance after the end of the period came to 0. So the Repayment amount is $ 58762.97

Hence Option a) $ 58762.97 is the Correct answer.

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