Multiple Choice
Which of the following best describes the concept of the time value of money?
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10. Time Value of Money
Time Value of Money Equations
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If you borrowed \$4,500 at an annual interest rate of 9.5\% for 1 year with a single payment due at the end of the year, what is the total amount you must repay at the end of the year?
A
\$4,500.00
B
\$5,000.00
C
\$4,927.50
D
\$4,282.50
Verified step by step guidance1
Step 1: Understand the problem. You are calculating the total repayment amount for a loan with simple interest. The formula for simple interest is: I = P × r × t, where I is the interest, P is the principal amount, r is the annual interest rate (expressed as a decimal), and t is the time in years.
Step 2: Identify the given values. From the problem, the principal amount (P) is $4,500, the annual interest rate (r) is 9.5% (convert this to decimal form as 0.095), and the time (t) is 1 year.
Step 3: Calculate the interest (I) using the formula I = P × r × t. Substitute the values: I = 4500 × 0.095 × 1.
Step 4: Determine the total repayment amount. The total repayment amount is the sum of the principal and the interest. Use the formula Total Repayment = P + I.
Step 5: Substitute the calculated interest (I) into the formula for Total Repayment to find the total amount you must repay at the end of the year.
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