Question

A principal of $2900 is invested at 3% interest, compounded annually. How many years will it take to accumulate $4000 or more in the account? (Use the calculator provided if necessary.)Write the smallest possible whole number answer.

Answer 1

To solve this problem, we will use the following formula for annually compounded interest:

$A=P(1+r)^t,$

where r is the rate of interest in decimal form, t is the number of years, and P is the initial amount.

Substituting P=2900, A=4000, r=0.03 in the formula, we get:

$\begin{gathered} 4000=2900(1+0.03)^t=2900(1.03)^t, \\ \frac{4000}{2900}=1.03^t. \end{gathered}$

Applying log to both sides of the equation we get:

$log(\frac{40}{29})=tlog1.03.$

Therefore:

$t=\frac{log\frac{40}{29}}{log1.03}\approx10.88\text{ years.}$

Rounding the smallest possible whole number, we get:

$t=11\text{ years.}$

Answer:

$11\text{ years.}$