Question

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On 31 October 2013, Josh borrowed money from his parents. He promised that he would repay...

On 31 October 2013, Josh borrowed money from his parents. He promised that he would repay the money on 31 October 2017, with interest at a nominal interest rate of 7% p.a., compounding quarterly. The total amount that he was due to pay his parents at that time was exactly $10,000 but he started his studies at university so he couldn’t afford to repay the loan. If interest continues to accrue, what amount must Josh pay on 31 October 2022 to fully pay off the loan?

Expert Solution

Given the Amount due on 31st October 2017 is $ 10,000

Rate of Interest per Year = 7% Compounding Quarterly

Interest rate Per Quarter = 7% /4 = 1.75%

The time gap between 31st October 2017 to 31st October 2022 is 5 years

Compounding Frequency = 4 times per year

Compounding Frequency during the tenure of 5 years = 5*4 = 20 times

S.No	Opening Balance	Interest accrued @ 1.75%	Closing Balance
1	$10,000	$175.00	$10,175.00
2	$10,175.00	$178.06	$10,353.06
3	$10,353.06	$181.18	$10,534.24
4	$10,534.24	$184.35	$10,718.59
5	$10,718.59	$187.58	$10,906.17
6	$10,906.17	$190.86	$11,097.02
7	$11,097.02	$194.20	$11,291.22
8	$11,291.22	$197.60	$11,488.82
9	$11,488.82	$201.05	$11,689.87
10	$11,689.87	$204.57	$11,894.44
11	$11,894.44	$208.15	$12,102.60
12	$12,102.60	$211.80	$12,314.39
13	$12,314.39	$215.50	$12,529.90
14	$12,529.90	$219.27	$12,749.17
15	$12,749.17	$223.11	$12,972.28
16	$12,972.28	$227.01	$13,199.29
17	$13,199.29	$230.99	$13,430.28
18	$13,430.28	$235.03	$13,665.31
19	$13,665.31	$239.14	$13,904.45
20	$13,904.45	$243.33	$14,147.78

Hence Josh should pay $ 14147.78 to repay the loan as on 31st October 2022

Alternative Method;

Future value = Present value ( 1+i/4)^4n, Here n = No.of Years

= $ 10000( 1+7/400)^4*5

= $ 10000( 1.0175)^20

= $ 10000*1.414778

= $14147.78

Hence Josh should pay $ 14147.78 to repay the loan as on 31st October 2022

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jeff jeffy answered 1 year ago

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