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?

Question

Mathematics

Gardner

2 August, 16:02

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?

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Answers (1)

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Lyric Cherry · Answer 1

8.5

Step-by-step 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.