Multiple Choice
What is the future value of \$1,200 invested for 20 years at an annual interest rate of 6%, compounded annually? (Use the formula: \(FV = PV \(\times\) (1 + r)^n\))
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10. Time Value of Money
Time Value of Money Equations
Multiple Choice
Which formula moves a cash flow of \$800 ahead six years in time at an interest rate of 5\%?
A
\(800 \div (1 + 0.05)^6\)
B
\(800 \times (1 + 0.05)^6\)
C
\(800 \div (1 - 0.05)^6\)
D
\(800 \times (1 - 0.05)^6\)
Verified step by step guidance1
Understand the concept: Moving a cash flow ahead in time involves calculating its future value using the formula for compound interest. The formula for future value is: FV = PV × (1 + r)^n, where PV is the present value, r is the interest rate, and n is the number of periods.
Identify the given values: The present value (PV) is \$800, the interest rate (r) is 5% or 0.05, and the number of periods (n) is 6 years.
Determine the correct formula: To move the cash flow ahead in time, we use the future value formula, FV = PV × (1 + r)^n. This formula accounts for compounding interest over the specified number of periods.
Compare the options provided: The correct formula matches FV = \$800 × (1 + 0.05)^6, as it uses the future value formula. The other options either divide the cash flow or use subtraction, which are incorrect for calculating future value.
Conclude the reasoning: The correct formula is \$800 × (1 + 0.05)^6 because it properly calculates the future value of the cash flow by compounding the interest rate over six years.
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