You currently have $2,200 (Present Value) in an account that has an interest rate of 5.5% per year compounded continuously. You want to withdraw all your money when it reaches $5,280 (Future Value).

Question

In how many years will you be able to withdraw all your money?

The number of years is?

Round your answer to 1 decimal place.

Answer 1

A = Pe^rt where A is $16600, P = $8300, r = 0.05 and t is the unknown.

16600 = 8300e^0.05t Divide by 8300

2 = e^0.05t Take natural log of both sides.

ln 2 = 0.05t (ln e) (ln e = 1)

0.6931 = 0.05t

t = 13.86 rounds to 13.9 years

You can check with a website with a continuous compounding calculator like Math Warehouse (I did!)

Answer 2

The formula for continuously compounded interest is:

P(t) = P₀·e^rt

1. P(t) = future value = $16,600
2. P₀ = present value = $8300
3. r = interest rate expressed as a decimal = 5% = 0.05
4. t = years

16,600 = 8300 e^0.05t

16,600/8300 = e^0.05t

2 = e^0.05t

Can you solve it from here? HINT: Take the natural log (ln) of both sides.