Multiple Choice
Which one of the following will decrease the present value of an annuity?
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10. Time Value of Money
Time Value of Money Equations
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What is the future value of an investment of \$2300 compounded continuously at an annual interest rate of 2\% for 3 years? (Use the formula \( FV = Pe^{rt} \))
A
\$2442.19
B
\$2438.00
C
\$2430.00
D
\$2410.00
Verified step by step guidance1
Understand the formula for continuous compounding: \( FV = Pe^{rt} \), where \( FV \) is the future value, \( P \) is the principal amount, \( r \) is the annual interest rate (in decimal form), \( t \) is the time in years, and \( e \) is the mathematical constant approximately equal to 2.718.
Identify the given values from the problem: \( P = 2300 \), \( r = 0.02 \) (convert 2% to decimal), and \( t = 3 \).
Substitute the values into the formula: \( FV = 2300 \cdot e^{0.02 \cdot 3} \).
Calculate the exponent first: \( 0.02 \cdot 3 = 0.06 \). Then, find \( e^{0.06} \) using a calculator or mathematical software.
Multiply the result of \( e^{0.06} \) by the principal \( 2300 \) to determine the future value \( FV \).
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