Multiple Choice
If you borrow \$20,000 for 5 years at an annual interest rate of 8\% compounded monthly, what would the monthly payment be?
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10. Time Value of Money
Time Value of Money Equations
Multiple Choice
What is the present value of \$1,000 to be received in 12 years, assuming an annual interest rate of 8\% compounded annually?
A
\$515.20
B
\$397.11
C
\$800.00
D
\$620.92
Verified step by step guidance1
Understand the concept of present value: Present value (PV) is the current worth of a future sum of money or stream of cash flows given a specified rate of return. It is calculated using the formula: PV = FV / (1 + r)^n, where FV is the future value, r is the annual interest rate, and n is the number of years.
Identify the given values from the problem: Future Value (FV) = \$1,000, annual interest rate (r) = 8% or 0.08, and the number of years (n) = 12.
Substitute the given values into the present value formula: PV = 1000 / (1 + 0.08)^12. This formula accounts for the compounding effect of interest over 12 years.
Simplify the denominator: Calculate (1 + 0.08)^12. This involves adding 1 to the interest rate (0.08) and raising the result to the power of 12.
Divide the future value (\$1,000) by the calculated denominator to determine the present value. This step completes the calculation, yielding the present value of \$1,000 to be received in 12 years at an 8% annual interest rate.
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