Question

You invest $270 in a mutual fund today that pays 9.00 percent interest annually. How long will it take to double your money? (If you solve this problem with algebra round intermediate calculations to 6 decimal places, in all cases round your final answer to 0 decimal place, e.g. 545)

Answer 1

Amount will be doubled in 8 years.

Explanation:

Since
`F=I(1+r)^(n)`

where F = final amount

I = initial amount or amount invested

r = rate of interest
`((r)/(100))`

n = Duration of investment in years

Now it has been given in the question

F = 270×2 = $540

I = $270

r = 0.09

We plug these values in the formula to get the value of n

`540=270(1+0.09)^(n)`

`(540)/(270)=(1.09)^(n)`

By taking log on both the sides

`log(2)=log(1.09)^(n)`

`log(2)=nlog(1.09)`

n =
`(log2)/(log1.09)`

=
`(0.30103)/(0.03743)`

= 8.04

≈ 8 years