Multiple Choice
Which of the following equations correctly calculates the future value ($FV$) of $1,000 invested today for 3 years at 5\% annual interest compounded annually?
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10. Time Value of Money
Time Value of Money Equations
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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?
A
\$931.70
B
\$513.00
C
\$525.66
D
\$700.00
Verified step by step guidance1
Step 1: Understand the problem. You are tasked with finding the value in year 3 of a $700 cash flow to be received in year 6, given an annual interest rate of 10% compounded annually. This involves discounting the future cash flow back to year 3 using the formula for present value.
Step 2: Recall the formula for present value (PV): \( PV = \frac{FV}{(1 + r)^n} \), where FV is the future value, r is the annual interest rate, and n is the number of years between the future value and the present value.
Step 3: Determine the number of years (n) between year 6 and year 3. Since year 6 is 3 years ahead of year 3, n = 3.
Step 4: Plug the given values into the formula. FV = $700, r = 0.10 (10%), and n = 3. The formula becomes \( PV = \frac{700}{(1 + 0.10)^3} \).
Step 5: Simplify the denominator by calculating \( (1 + 0.10)^3 \), then divide $700 by the result to find the present value in year 3. This will give you the value of the cash flow in year 3.
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