Multiple Choice
Other things being equal, which of the following will produce the greatest future value for a single sum invested today?
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10. Time Value of Money
Time Value of Money Equations
Multiple Choice
Janet takes out a loan of \$10,000 at an annual interest rate of 6ext{%}, to be repaid in equal monthly installments over 5 years. By the time Janet pays off her entire loan, how much total interest will she have paid?
A
\$6,000
B
\$2,500
C
\$1,600
D
\$3,199
Verified step by step guidance1
Step 1: Understand the problem. Janet has taken out a loan of \$10,000 at an annual interest rate of 6%. She will repay the loan in equal monthly installments over 5 years. The goal is to calculate the total interest paid over the life of the loan.
Step 2: Calculate the monthly interest rate. The annual interest rate is 6%, so divide it by 12 to find the monthly interest rate: \( \text{Monthly Interest Rate} = \frac{6}{100 \times 12} \).
Step 3: Determine the total number of payments. Since the loan is repaid over 5 years with monthly installments, multiply the number of years by 12: \( \text{Total Payments} = 5 \times 12 \).
Step 4: Use the formula for the monthly payment of a loan. The formula is \( M = \frac{P \cdot r \cdot (1 + r)^n}{(1 + r)^n - 1} \), where \( M \) is the monthly payment, \( P \) is the loan principal (\$10,000), \( r \) is the monthly interest rate, and \( n \) is the total number of payments.
Step 5: Calculate the total amount paid over the life of the loan by multiplying the monthly payment \( M \) by the total number of payments \( n \). Subtract the original loan principal from this total to find the total interest paid: \( \text{Total Interest} = (M \times n) - P \).
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