Compounding — Solve for Time

Question

Jose invested $1,100 in an account paying an interest rate of 2.6% compounded monthly. 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 $1,630?

Answer 1

When dealing with compound interest use the follow formula:

A = P (1 + r/n) ^(nt)

A = amount, P = principal (starting amount invested), r = interest rate (in decimal form), n = # of times compound per year (monthly is 12 times per year), t = time. Plug all given information into the formula.

1,630 = 1,100 (1 + .026/12)^(12 * t) First, divide both sides by 1,100 and simplify inside the parentheses

1.4818 = (1.00217)^(12*t) Now to solve for an exponent, we have to add a log to both sides

log(1.4818) = (12*t) * log(1.00217) Now divide both sides by the log on the right side

log(1.4818) / log(1.00217 ) = 12t Plug the left hand side into your calculator

181.4212421 = 12t Last step is to divide by 12 and round to 1 decimal place

t = 15.1 years