Multiple Choice
Which of the following time value of money equations is most appropriate for a manager to use when forecasting future operating income based on current income and a constant growth rate?
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10. Time Value of Money
Time Value of Money Equations
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Charlie invests $5,000 in an account that earns 6\% annual interest, compounded annually. Which of the following amounts is closest to the value of Charlie’s investment after 40 years?
A
$32,000
B
$51,429
C
$12,000
D
$18,000
Verified step by step guidance1
Understand the problem: Charlie's investment grows with compound interest. The formula for compound interest is \( A = P(1 + r)^t \), where \( A \) is the future value, \( P \) is the principal amount, \( r \) is the annual interest rate, and \( t \) is the time in years.
Identify the given values: \( P = 5000 \), \( r = 0.06 \) (6% annual interest), and \( t = 40 \) years. Substitute these values into the formula.
Break down the formula substitution: \( A = 5000(1 + 0.06)^{40} \). First, calculate \( 1 + 0.06 \), which equals \( 1.06 \). Then raise \( 1.06 \) to the power of \( 40 \).
Multiply the result of \( 1.06^{40} \) by \( 5000 \) to find the future value of Charlie's investment.
Compare the calculated future value to the provided options \( \{32000, 51429, 12000, 18000\} \) and determine which is closest to the computed value.
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