Question

Hunter borrows $60,000 from a bank and wishes to pay it back with 10 equal annual payments. The annual effective interest rate of i=.085. a) If Hunter pays back the $60,000 loan with equal payments at the beginning of each year (first payment is due when the $60,000 loan is received), what should Hunter's annual payment be? b) If Hunter pays back the $60,000 loan with equal payments at the end of each year (first payment is due one year after receipt of the $60,000 loan), what should Hunter's annual payment be? 2) Same as question 1, but Hunter pays back the $60,000 loan with equal monthly payments at the end of each of each month for 10 years (first payment is due one month after receipt of the $60,000 loan). If i=.085, what should Hunter's monthly payment be? 3) Jingyun opens a new bank account on 1/1/2017 and deposits $75 in the account on the first day of every month, with the first deposit on 1/1/2017 and the last deposit on 12/1/2022. If i

(6)
=.072, and assuming no withdrawals are made, what is the accumulated value of the account on 12/31/2022?

Answer 1

Hunter's annual or monthly repayment amounts for a $60,000 loan at 8.5% interest rate and Jingyun's accumulated bank account value can be calculated using annuity formulas: annuity due and ordinary annuity for Hunter's scenario, and future value of an annuity for Jingyun's deposits.

Step-by-step explanation:

Loan Repayment Calculations

To calculate Hunter's repayments for a $60,000 loan at an effective annual interest rate of 8.5% to be repaid over 10 years, we can use various formulas for annuities.

Part a) Annual Payments at the Beginning of Each Year

Hunter is making payments at the beginning of each period, which is an annuity due scenario. To find the annual payment, we use the present value formula for an annuity due: PV = R[1 + i × (1 − (1 + i)^−n) / i]. Solving for R gives us the regular payment Hunter must make.

Part b) Annual Payments at the End of Each Year

For payments at the end of each year, we use the ordinary annuity formula: PV = R[(1 − (1 + i)^−n) / i]. Again, we solve for R to find Hunter's payment.

Part 2) Monthly Payments

For equal monthly payments, we first convert the annual interest rate to a monthly rate by dividing by 12. Since the payments are at the end of each period, we use the ordinary annuity formula with the monthly interest rate and number of periods (120).

Part 3) Accumulated Value of Jingyun's Bank Account

Jingyun makes monthly deposits into an account with a semi-annual interest rate of 7.2%. To calculate the accumulated value, we use the future value formula of an annuity for monthly deposits: FV = d[[(1 + i)^n - 1] / i], where i is the monthly interest rate and n is the total number of deposits made.