Compounding — Solve for Time

Question

Zachary invested $63,000 in an account paying an interest rate of 5.3% 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 $138,800?

Answer 1

The formula for continuous compounding is A = Pe^rt

If we plug in the values we know

138800 = 63000e^0.053t

Now to solve for t, Divide both sides of the equation by 63000 and simplify

138800/63000 = 63000/63000e^0.053t

138800/63000 = e^0.053t

Take the ln of both sides of the equation

ln(138800/63000) = ln e^0.053t

The exponent moves to the front of the equation and ln e = 1

ln(138800/63000) = (0.053t)ln e

Divide both sides of the equation by 0.053 to solve for t

[ln(138800/63000)]/0.053 = (0.053t)/0.053

t=14.9 years

Answer 2

A=P.e^rt

if we use the following formula and plug in the given values, we would get the answer approximately 15 years to the nearest whole year.By the way, if you need to find the time you are going to have to take ln of both sides so you get rid of exponent.