Jackson deposited $100 in a savings account that pays 6% interest compounded continuously. He just withdrew the entire balance of $200. How long ago did he open the account?

Question

asked Jan 9, 2024 39.1k views

2 Answers

Lars Dol · Answer 1 · 2024-01-13T11:04:32+0000

Answer:

11.6 years

Explanation:

You want to know the time it takes to double an account value when it earns interest at 6% compounded continuously.

The formula for the value of an account earning compound interest is ...

A = Pe^(rt)

where P is invested at rate r for t years.

200 = 100e^(.06t) . . . . . use the given values

ln(200/100) = 0.06t . . . . . take natural logs

t = ln(2)/.06 ≈ 11.6

The account was opened about 11.6 years ago.

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