Multiple Choice
If you are to receive \$20,000 in 50 years, what is its present value today assuming a discount rate of 7.5\% compounded annually?
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10. Time Value of Money
Time Value of Money Equations
Multiple Choice
If you invest \$100 at an annual interest rate of 5\% compounded once per year, how much will it be worth after 75 years?
A
\$1,000.00
B
\$2,000.00
C
\$500.00
D
\$3,248.39
Verified step by step guidance1
Step 1: Understand the formula for compound interest, which is \( A = P(1 + r)^t \), where \( A \) is the future value, \( P \) is the principal amount, \( r \) is the annual interest rate (in decimal form), and \( t \) is the number of years.
Step 2: Identify the values given in the problem: \( P = 100 \), \( r = 0.05 \) (5\% expressed as a decimal), and \( t = 75 \).
Step 3: Substitute the values into the formula: \( A = 100(1 + 0.05)^{75} \).
Step 4: Simplify the expression inside the parentheses: \( 1 + 0.05 = 1.05 \). The formula now becomes \( A = 100(1.05)^{75} \).
Step 5: Calculate \( (1.05)^{75} \) and then multiply the result by \( 100 \) to find the future value. This will give you the final amount after 75 years.
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