Question

1000 was invested at 5.5% interest, compounded annually. After sometime the amount had grown to 1550. How long was the money invested?

Answer 1

compound interest equation for annually compounded

`A=P(1+r)^t`

A=final amount

P=principal

r=rate in decimal

t=time in years

given that

A=1550

P=1000

r=5.5%=0.055

find t

`1550=1000(1+0.055)^t`

divide both sides by 1000

`1.55=1.055^t`

take ln of both sides

`ln(1.55)=ln(1.055^t)`

use ln rule
`ln(a^b)=b(ln(a))`

`ln(1.55)=t(ln(1.055))`

divide both sides by ln(1.055)

`(ln(1.55))/(ln(1.055))=t`

using a calculator, we get that t=8.18544 yrs

so about 8.2yrs