Multiple Choice
What annual interest rate, compounded annually, will cause your money to double in four years?
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10. Time Value of Money
Time Value of Money Equations
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What is the future value of \$100 compounded annually for 50 years at an annual interest rate of 10\%? (Use the formula: \( FV = PV \times (1 + r)^n \))
A
\$11,739.09
B
\$10,000.00
C
\$1,170.00
D
\$5,000.00
Verified step by step guidance1
Step 1: Identify the variables in the formula for future value (FV = PV × (1 + r)^n). Here, PV (Present Value) is $100, r (annual interest rate) is 10% or 0.10, and n (number of years) is 50.
Step 2: Convert the annual interest rate from a percentage to a decimal by dividing by 100. For example, 10% becomes 0.10.
Step 3: Add 1 to the interest rate (r). This gives (1 + r), which is (1 + 0.10) = 1.10.
Step 4: Raise (1 + r) to the power of n (number of years). This means calculating (1.10)^50.
Step 5: Multiply the Present Value (PV) by the result from Step 4. This gives FV = 100 × (1.10)^50.
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