Compounding — Solve for Time

Question

Zoe invested $100 in an account paying an interest rate of 6% compounded daily. 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 $160?

Answer 1

A=P(1+r/n)nt, since we use compound interest daily, we are going to use 365 for n.

n=365

p=100

r=0.06

a=160

let's plug all those value into the formula.

160=100.(1.000164)^365t

if you divide each side by 100 and take log each side to get t by itself on the right hand side, we would get the following

1.6=365t*log(1.000164)

if we solve the equation for t , we would get t=61.6 years