Question

Neslihan has borrowed $1,000,000 from MQ Bank for 10 years at an interest rate of j =3.11%. She will make 10 annual repayments. According to the loan agreement, Neslihan's repayments will be $94,000 for the first two years followed by payments of with the amount of X per year for the remaining eight years. This loan needs to be fully repaid by the end of 10 years. (a) Assume that all annual repayments will be paid at the end of each year (the first payment will be at the end of the first year), what is the value of Neslihan's annual payment amount X (rounded to four decimal places) a. 125029.1998 b. 117545.5547 c. 117417.0375 d. 124833.9442

Answer 1

In order to calculate the value of Neslihan's annual payment amount X, we need to find the present value of the loan and equate it to the future value of the repayments. By using the formula for present value of an annuity and setting up the appropriate equation, we can solve for X.

Step-by-step explanation:

To find the value of Neslihan's annual payment amount X, we need to calculate the present value of the loan and equate it to the future value of the annual repayments. The present value of the loan is the sum of the present values of the $94,000 repayments for the first two years and the present value of the remaining eight years' repayments. Using the formula for present value of an annuity, we can calculate X.

The present value of the $94,000 repayments for the first two years is $94,000 + $94,000 / (1 + 0.0311) + $94,000 / (1 + 0.0311)^2.

The present value of the remaining eight years' repayments is X / (1 + 0.0311)^3 + X / (1 + 0.0311)^4 + ... + X / (1 + 0.0311)^10.

By equating the present value of the loan to the present value of the repayments, we can solve for X:

$1,000,000 = $94,000 + $94,000 / (1 + 0.0311) + $94,000 / (1 + 0.0311)^2 + X / (1 + 0.0311)^3 + X / (1 + 0.0311)^4 + ... + X / (1 + 0.0311)^10

Solving this equation will give us the value of X, which can be rounded to four decimal places.