Question

Olivia invested $2,400 in an account paying an interest rate of 4.6\% compounded continuously. Assuming no deposits or withdrawals are made, how long would it take, to the nearest tenth of a year, for the value of the account to reach $3,550 ?

Answer 1

8.5

Explanation:

For continuous compounding, the account value formula is ...

A = Pe^(rt)

where P is the invested amount, r is the annual interest rate, and t is the number of years. We want to find t when ...

3550 = 2400e^(.046t)

ln(355/240) = 0.046t

t = ln(355/240)/0.046 ≈ 8.5

It will take 8.5 years for the value to reach $3550.