Practice Problem – Compound Interest

Practice Question

Intro to Finance
Time Value of Money
Compound Interest, Future Value
Short Answer

How long will it take to double your money if you deposit it in a savings account which gives you 2% per year interest (compounded semiannually)?

Answer +
Correct Answer: 34.83 years
Explanation +
Step 1: Use the Compound Interest Formula

The formula for future value is:

FV = PV × (1 + r/m)m × n

Where:

  • FV = 2 × PV (since we want to double the money)
  • r = 0.02 (annual interest rate)
  • m = 2 (compounded semiannually)
  • n = number of years
Step 2: Plug in the Known Values

2 = (1 + 0.02 / 2)2n → 2 = (1.01)2n

Step 3: Take the Natural Log of Both Sides

ln(2) = 2n × ln(1.01)

n = ln(2) / (2 × ln(1.01))

Step 4: Final Calculation

n = 0.693147 / (2 × 0.009950) = 34.83

Final Answer:

It will take approximately 34.83 years to double your money.