Question

Timber Inc. invested profits of $220,000.00 in a GIC at 4.09% compounded monthly. How long will it take for the investment to grow to a value of at least $306,000.00?___years and ___months

Answer 1

Compound Interest

Timber Inc. invested PV=$220,000 in a GIC at a rate of r=4.09% compounded monthly. We need to find the time it takes for the investment to have a value of FV=$306,000.

Recall PV is the present value of an investment, FV is its future value, r is the nominal interest rate, r = 0.0409 when expressed in decimal, and m = 12 because there are 12 compounding periods per year.

The periodic interest rate is calculated as:

`i=(r)/(m)=(0.0409)/(12)=0.00340833`

Here it's important to preserve as many decimals as possible because rounding can affect the ongoing calculations.

From the formula of the future value:

`FV=PV(1+i)^n`

Where n is the number of compounding periods of the investment, we can solve for n as follows:

`n=(\ln ((FV)/(PV)))/(\ln (1+i))`

Substituting:

`n=(\ln ((306,000)/(220,000)))/(\ln (1+0.00340833))\approx97`

The investment should last for 97 months. Since one year has 12 months, 97 months represent 97/12 = 8 whole years. The remainder of this division is 1, so the time expressed in years+months is: 8 years and 1 month