Nikita takes out a 10-year loan. The loan is repaid by making 10 annual repayments at...

Nikita takes out a 10-year loan. The loan is repaid by making 10 annual repayments at the end of each year. The first loan repayment is equal to X, with each subsequent repayment 10.16% greater than the previous year’s repayment. The annual effective interest rate being charged on the loan is 8%. The amount of interest repaid during the first year is equal to 892.20. Calculate X.

a.1100

b.1150

c.1200

d.1250

e.1300

Solutions

Expert Solution

Principal = Int / Int rate

= $ 892.20 / 8%

= $ 11152.50

Loan Amount = PV of CFs at int Rate.

Year	CashFlow	PVF @8%	PV of CFs
1	x	0.9259	0.9259x
2	1.1016x	0.8573	0.9444x
3	1.2135x	0.7938	0.9633x
4	1.3368x	0.7350	0.9826x
5	1.4726x	0.6806	1.0023x
6	1.6223x	0.6302	1.0223x
7	1.7871x	0.5835	1.0427x
8	1.9686x	0.5403	1.0636x
9	2.1687x	0.5002	1.0849x
10	2.389x	0.4632	1.1066x
Loan Amount			10.1377x

Thus 10.1377x = $ 11152.50

x = 11152.50 / 10.1377

= $ 1100.10 I.e $ 1100

Option A is correct

jeff jeffy answered 1 year ago

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