Multiple Choice
What is the value in year 3 of a \$700 cash flow to be received in year 6, assuming an annual interest rate of 10\% compounded annually?
113
views
10. Time Value of Money
Time Value of Money Equations
Multiple Choice
Which of the following equations correctly calculates the future value (FV) of \$1,000 invested today for 5 years at an annual interest rate of 4.3% compounded annually?
A
FV = 1,000 \(\times\) (1 + 0.043)^5
B
FV = 1,000 \(\times\) (1 - 0.043)^5
C
FV = 1,000 \(\times\) (1 + 0.043 \(\times\) 5)
D
FV = 1,000 \(\div\) (1 + 0.043)^5
Verified step by step guidance1
Step 1: Understand the concept of future value (FV). Future value is the value of an investment at a specific point in the future, considering the interest earned over time. When interest is compounded annually, the formula for FV is: FV = PV × (1 + r)^n, where PV is the present value, r is the annual interest rate, and n is the number of years.
Step 2: Analyze the given options. The correct formula for FV must include compounding, which means the interest is applied to the principal and accumulated interest over multiple periods. This is represented by the term (1 + r)^n.
Step 3: Eliminate incorrect options. For example, FV = 1,000 × (1 - 0.043)^5 is incorrect because it subtracts the interest rate instead of adding it. Similarly, FV = 1,000 × (1 + 0.043 × 5) is incorrect because it assumes simple interest rather than compounding. FV = 1,000 ÷ (1 + 0.043)^5 is incorrect because it divides instead of multiplying.
Step 4: Identify the correct formula. The correct formula is FV = 1,000 × (1 + 0.043)^5, as it properly accounts for annual compounding over 5 years.
Step 5: Apply the formula conceptually. To calculate the future value, substitute the values into the formula: PV = 1,000, r = 0.043, and n = 5. The calculation involves raising (1 + 0.043) to the power of 5 and then multiplying the result by 1,000.
Related Videos
Related Practice
