Gina puts $ 4500 into an account earning 7.5% interest compounded continuously. How long will it take for the amount in the account to grow to $ 5150?

Question

Gina puts $ 4500 into an account earning 7.5% interest compounded continuously. How long will it take for the amount in the account to grow to $ 5150?

Time in years =

Answer 1

Hello Gabrille, you have to use the continuous compounding formula:

A = Pe^rt where A is the final amount; P is the principal aka original amount invested; r is the interest rate, t is the duration of the investment.

"Gina puts $4500 into an account" - this tells you P = 4500

"...an account earning 7.5% interest compounded continuously" - this tells you r = 7.5% = 0.075

"How long will it take for the amount in the account to grow to $ 5150?" - this tells you A = 5150 and asks you to solve for t.

5150 = 4500 e^0.075t

Divide both sides by 4500: (5150/4500) = e^0.075t vv

take natural log of both sides: ln (5150/4500) = 0.075t

Divide both sides by 0.075: t = ln(5150/4500) / 0.075

Put it in a calculator and you get t = 1.79892423 years

I'll let you round the answer accordingly. You got this.