Question

3) An $1,000 investment is made in a trust fund at an annual percentage rate of 12%,

compounded yearly. How long will it take the investment to reach $2,000?

Answer 1

We need to find the interest rate in order to solve this problem:

.12/12 = (.01)

The number of years is unknown. T represents time in the following formula:

1000 (initial investment)

2000 (balance after t years from investment)

`$1000 (1 + .01)^(12t)`=$2000

In order to isolate the exponential term, both sides must be divided by 1000.

`(1+.01)^(12t)`=2

By using natural logarithm:

`Ln(1+.01)^(12t) =Ln2\\(12t)Ln(1+.01)=Ln2\\`

By dividing both sides of the equation by
`(12)Ln(1+.01)`

`t=(Ln(2))/((12)Ln(1+.01)) =5.805yrs`