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Multiple Choice
What is the present value of \$100 to be received in 8 years if the annual interest rate is 5\% compounded annually?
A
\$85.00
B
\$55.00
C
\$67.68
D
\$80.00
Verified step by step guidance
1
Understand the concept of present value: Present value (PV) is the current worth of a future sum of money given a specific interest rate and time period. 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) = $100, annual interest rate (r) = 5% or 0.05, and the time period (n) = 8 years.
Substitute the given values into the present value formula: PV = 100 / (1 + 0.05)^8.
Simplify the denominator: Calculate (1 + 0.05)^8, which represents the compounding effect of the interest rate over 8 years.
Divide the future value ($100) by the calculated denominator to find the present value. This will give the current worth of $100 to be received in 8 years at a 5% annual interest rate.