Multiple Choice
The amount of interest paid is normally calculated on which of the following?
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10. Time Value of Money
Time Value of Money Equations
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If you want to have \$820 in 3 years, how much should you invest now at an annual interest rate of 5\% compounded continuously?
A
\$780.95
B
\$700.00
C
\$820.00
D
\$705.37
Verified step by step guidance1
Understand the formula for continuous compounding: \( P = A \cdot e^{-rt} \), where \( P \) is the present value, \( A \) is the future value, \( r \) is the annual interest rate, \( t \) is the time in years, and \( e \) is the mathematical constant approximately equal to 2.718.
Identify the given values from the problem: \( A = 820 \), \( r = 0.05 \) (5% annual interest rate), and \( t = 3 \) years.
Substitute the given values into the formula: \( P = 820 \cdot e^{-0.05 \cdot 3} \).
Calculate the exponent \( -0.05 \cdot 3 \) to determine the power of \( e \).
Multiply the future value \( 820 \) by \( e \) raised to the calculated power to find the present value \( P \).
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