Question

George wants to save money for a car. George invests $1,400 in an account that pays an interest rate of 6.25%.

How many years will it take for the account to reach $15,400? Round your answer to the nearest hundredth.

Answer 1

It will take 39.55 years

Explanation:

We have

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

where A is the total amount, P is the principal, r is the annual interest, n is the number of times compounded anually and t is the total years

For our question, we have:

A = 15400

P = 1400

r = 6.25% = 0.0625

n = 1

t = ?

so,

`15400 = 1400(1+ (0.0625)/(1) )^(t)\\\\(15400)/(1400) = 1.0625^t\\\\1.0625^t = 11\\\\Taking \;\;log,\\\\log(1.0625^t) = log(11)\\\\t \;log(1.0625) = log(11)\\\\t = (log(11))/(log(1.0625))\\ \\t = 39.55`