Question

In: Finance

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


Related Solutions

Donald takes out a loan to be repaid with annual payments of $500 at the end...
Donald takes out a loan to be repaid with annual payments of $500 at the end of each year for 2n years. The annual effective interest rate is 4.94%. The sum of the interest paid in year 1 plus the interest paid in year n + 1 is equal to $720. Calculate the amount of interest paid in year 10.
A loan of $100,000 is made today. This loan will be repaid by 10 level repayments,...
A loan of $100,000 is made today. This loan will be repaid by 10 level repayments, followed by a final smaller repayment, i.e., there are 11 repayments in total. The first of the level repayments will occur exactly 2 years from today, and each subsequent repayment (including the final smaller repayment) will occur exactly 1 year after the previous repayment. Explicitly, the final repayment will occur exactly 12 years from today. If the interest being charged on this loan is...
A loan of $100,000 is made today. This loan will be repaid by 10 level repayments,...
A loan of $100,000 is made today. This loan will be repaid by 10 level repayments, followed by a final smaller repayment, i.e., there are 11 repayments in total. The first of the level repayments will occur exactly 2 years from today, and each subsequent repayment (including the final smaller repayment) will occur exactly 1 year after the previous repayment. Explicitly, the final repayment will occur exactly 12 years from today. If the interest being charged on this loan is...
Jenny takes out a 10-year loan of 100,000 at an annual effective rate of 8%. At...
Jenny takes out a 10-year loan of 100,000 at an annual effective rate of 8%. At the end of each year Jenny makes interest payments to the lender and sinking fund deposits into a sinking fund earning 6% annual effective. Jenny's first sinking fund deposit is $1000 and the remaining deposits are level. a) Find the total (net) interest paid on the loan. b) How would the total (net) interest paid on the loan change if the interest rate on...
Susana takes out a $1,000 loan. The loan carries a 10% annual interest rate and it...
Susana takes out a $1,000 loan. The loan carries a 10% annual interest rate and it will be amortized with fixed annual payments over a five-year period. Construct the amortization schedule for this loan? What is the fraction of the fixed payment represent the repayment of principal in year 2? Assume Annual Compounding Show Formula Find Annual Payment Create Amortization Table Show fraction of the fixed payment represents the repayment of principal in year 2
A 35-year loan is to be repaid by half-yearly repayments of 1,000 starting in 6 months...
A 35-year loan is to be repaid by half-yearly repayments of 1,000 starting in 6 months at an interest rate of 9.0% p.a. compounded half yearly. Or, it can be repaid by year-end repayments of $X staring in one year. Calculate the yearly repayments $X. Correct your answer to the nearest cent without any units. (Do not use "$" or "," in your answer. e.g. 12345.67)?
You take out a loan in the amount of $260,000 with annual equal repayments over the...
You take out a loan in the amount of $260,000 with annual equal repayments over the next 20years. What is the balance of the loan after the 5th payment? i = 6%
A loan is to be repaid over 30 years, with month-end repayments of 3,000. If the...
A loan is to be repaid over 30 years, with month-end repayments of 3,000. If the interest rate is 6.5% p.a. compounded monthly. Calculate the principal paid for year 10. Correct your answer to the nearest cent without any units. (Do not use "$" or "," in your answer. e.g. 12345.67)  
A loan is to be repaid over 30 years, with month-end repayments of 9,000. If the...
A loan is to be repaid over 30 years, with month-end repayments of 9,000. If the interest rate is 7.0% p.a. compounded monthly. Calculate the interest paid for year 10. Correct your answer to the nearest cent without any units. (Do not use "$" or "," in your answer. e.g. 12345.67)  
A loan is to be repaid over 30 years, with month-end repayments of 8,000. If the...
A loan is to be repaid over 30 years, with month-end repayments of 8,000. If the interest rate is 3.8% p.a. compounded monthly. Calculate the interest paid for year 10. Correct your answer to the nearest cent without any units. (Do not use "$" or "," in your answer. e.g. 12345.67)
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT