Multiple Choice
Ava charges \$1,200 to her credit card, which has an annual interest rate of 18% compounded monthly. If she pays off the entire balance in 11 months, how much total interest will she pay?
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10. Time Value of Money
Time Value of Money Equations
Multiple Choice
What is the value of a \$1 single sum to be received in 5 years, discounted at an annual interest rate of 8% compounded annually?
A
\$0.80
B
\$0.46
C
\$0.68
D
\$1.08
Verified step by step guidance1
Identify the formula for calculating the present value of a single sum: \( PV = \frac{FV}{(1 + r)^n} \), where \( PV \) is the present value, \( FV \) is the future value, \( r \) is the annual interest rate, and \( n \) is the number of years.
Substitute the given values into the formula: \( FV = 1 \), \( r = 0.08 \) (8% annual interest rate), and \( n = 5 \) years.
Simplify the denominator by calculating \( (1 + r)^n \): \( (1 + 0.08)^5 \).
Divide the future value (\( FV = 1 \)) by the result of \( (1 + 0.08)^5 \) to find the present value.
Interpret the result as the present value of \$1 to be received in 5 years, discounted at an annual interest rate of 8% compounded annually.
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