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 $(12)Ln(1+.01)$

$t=\frac{Ln(2)}{(12)Ln(1+.01)} =5.805yrs$