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
$\frac{63}{47} =(1.045)^t$
take the ln of both sides
$ln(\frac{63}{47}) =ln((1.045)^t)$
$ln(\frac{63}{47}) =t(ln(1.045)$
divide both sides by ln(1.045)
$\frac{ln(\frac{63}{47})}{ln(1.045)}=t$
using calculator
6.656=t
so after about 6.7 years