Question

Compute the future value of a $100 cash flow for the following combinations of rates and times.

a. r=8%, t=10 years
b. r=8%, t=20 years
c. r=4%, t=10 years
d. r=4%, t=20 years

Answer 1

The future value of a $100 cash flow varies based on the interest rate and time, with calculations for 8% at 10 and 20 years yielding $215.89 and $466.10 respectively, and 4% at those same intervals yielding $148.02 and $219.11 respectively.

Step-by-step explanation:

To compute the future value of a $100 cash flow, we use the formula: Future Value = Present Value × (1 + Interest Rate)Number of Years, where Present Value is the initial amount, the Interest Rate is the annual rate, and the Number of Years is the time period over which the money is invested.

• a. r=8%, t=10 years: Future Value = $100 × (1 + 0.08)10 = $100 × (1.08)10 = $215.89
• b. r=8%, t=20 years: Future Value = $100 × (1 + 0.08)20 = $100 × (1.08)20 = $466.10
• c. r=4%, t=10 years: Future Value = $100 × (1 + 0.04)10 = $100 × (1.04)10 = $148.02
• d. r=4%, t=20 years: Future Value = $100 × (1 + 0.04)20 = $100 × (1.04)20 = $219.11

These calculations show that higher interest rates and longer investment periods lead to substantially more future value accrued thanks to the power of compounding interest.