Multiple Choice
What is the present value of a \$600 annuity payment received at the end of each year for 4 years, if the interest rate is 6\% per year?
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10. Time Value of Money
Time Value of Money Equations
Multiple Choice
If John takes out a \$10,000 loan at an annual interest rate of 6\% compounded annually for 5 years and repays the loan in equal annual installments, how much total interest will he pay over the course of the loan?
A
\$3,000
B
\$2,000
C
\$1,598.50
D
\$1,500
Verified step by step guidance1
Step 1: Understand the problem. John is repaying a loan of \$10,000 with an annual interest rate of 6% compounded annually over 5 years. The goal is to calculate the total interest paid over the course of the loan. This involves determining the equal annual installment amount and then calculating the total interest paid.
Step 2: Use the formula for calculating the equal annual installment (annuity payment) for a loan. The formula is: \( A = \frac{P \cdot r}{1 - (1 + r)^{-n}} \), where \( A \) is the annual installment, \( P \) is the loan principal, \( r \) is the annual interest rate divided by 100, and \( n \) is the number of years.
Step 3: Substitute the values into the formula. Here, \( P = 10,000 \), \( r = \frac{6}{100} = 0.06 \), and \( n = 5 \). Calculate \( A \), the annual installment amount.
Step 4: Multiply the annual installment amount \( A \) by the number of years \( n \) to find the total amount repaid over the course of the loan. Then subtract the original loan principal \( P \) from the total amount repaid to determine the total interest paid.
Step 5: Verify the calculation by ensuring the total interest paid matches the correct answer provided in the problem, which is \$1,598.50.
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