Multiple Choice
In an annuity, the accumulated money is converted into which of the following values using the time value of money equations?
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10. Time Value of Money
Time Value of Money Equations
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What is the future value of $1,000 invested for 15 years at an annual interest rate of 5%, compounded annually?
A
$2,078.93
B
$2,079.00
C
$1,500.00
D
$1,750.00
Verified step by step guidance1
Identify the formula for future value with annual compounding: \( FV = PV \times (1 + r)^n \), where \( FV \) is the future value, \( PV \) is the present value, \( r \) is the annual interest rate, and \( n \) is the number of years.
Substitute the given values into the formula: \( PV = 1000 \), \( r = 0.05 \) (5% as a decimal), and \( n = 15 \). The formula becomes \( FV = 1000 \times (1 + 0.05)^{15} \).
Simplify the expression inside the parentheses: \( 1 + 0.05 = 1.05 \). The formula now becomes \( FV = 1000 \times (1.05)^{15} \).
Calculate the exponent \( (1.05)^{15} \) to determine the growth factor over 15 years.
Multiply the result of \( (1.05)^{15} \) by \( 1000 \) to find the future value of the investment.
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