Multiple Choice
Which term describes the process of converting an annuity's accumulated value into a periodic income stream?
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10. Time Value of Money
Time Value of Money Equations
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What is the future value of $2, invested at an annual interest rate of 5\% compounded annually for 3 years?
A
$2.25
B
$2.15
C
$2.30
D
$2.31
Verified step by step guidance1
Understand the formula for future value (FV) when interest is compounded annually: \( FV = PV \times (1 + r)^n \), where PV is the present value, r is the annual interest rate (in decimal form), and n is the number of years.
Identify the values given in the problem: Present Value (PV) = $2, annual interest rate (r) = 5\% or 0.05, and the number of years (n) = 3.
Substitute the values into the formula: \( FV = 2 \times (1 + 0.05)^3 \).
Simplify the expression inside the parentheses: \( 1 + 0.05 = 1.05 \), then raise it to the power of 3: \( 1.05^3 \).
Multiply the result of \( 1.05^3 \) by the present value (PV = $2) to calculate the future value (FV).
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