In: Finance
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
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