How long do they need to wait before being able to pay for the trip?

Question

Kenji and Carmen Deposit $800 into a savings account which earns 1% interest compounded continuously. They want to use the money in the account to go on a trip that costs $1300. How long will they need to wait before being able to pay for the trip?

Answer 1

Continuous Compounding formula: A = Pe^rt, where P = the amount you invest, r = interest rate = %/100, t = time in years and A = amount you want to receive.

Input what you know into the formula: 1300 = 800 e^.01t

Divide by 800: 1.625 = e^.01t

To find an exponent (t), log both sides using the natural log because of "e": ln (1.625) = ln e^.01t

Use the logarithmic property ln e^x = x: ln (1.625) = .01t

Divide by .01 to solve for t: t = (ln(1.625))/.01 ≈ 48.551 years

Answer: ≈ 48.6 years (a long time at 1% interest)

Answer 2

fv=p(1+int/c)^(nt)

1300=800(1+.01/365)^(365*n)

n=27yrs

They need a better deal.