Question

A loan of $47,000 is made at 4.5% interest, compounded annually. After how many years will the amount due reach $63,000 or more?

Answer 1

`A=P(1+r)^t` is comounded yearly formula

rat ie 4.5%
P=47000
solve for when A=63000




`63000=47000(1+0.045)^t`
divide both sides by 47000

`(63)/(47) =(1.045)^t`
take the ln of both sides

`ln((63)/(47)) =ln((1.045)^t)`

`ln((63)/(47)) =t(ln(1.045)`
divide both sides by ln(1.045)

`(ln((63)/(47)))/(ln(1.045))=t`
using calculator
6.656=t
so after about 6.7 years