Question

If Debbie starts a retirement account with 10,000 dollars that has an annual rate of return of 12%, how long (in years) would it take for her to have at least 100,000 dollars if interest is compounded continuously?

Answer 1

19.2 years

Explanation:

The formula to find the time in a compound interest that is compounded continuously is given as:

t = ln(A/P) / r

Where:

t = time in years = ??

A = Amount after Interest is compounded continuously = $100,000

P = Initial Amount in the retirement account = $10,000

r = Rate of return = 12%

First, convert R percent to r a decimal

r = R/100

r = 12%/100

r = 0.12 per year,

Then, solve our equation for t

t = ln(A/P) / r

t = ln(100,000.00/10,000.00) / 0.12

t = 19.188 years

Approximately t = 19.2 years