Question

A thousand dollars is left in a credit union drawing 7% compounded monthly, how many years will it need to be left to produce an ending balance of $2500?

Answer 1

Explanation:

For compound interest, we have the following equation

$A=P(1+\frac{r}{n})^{nt}$

Where A is the amount after t years, P is the initial amount, r is the interest rate and n is the number of times the interest is compound.

In this case, we know

A = $2500

P = $1000

r = 7% = 0.07

n = 12 (compounded monthly)

t = ?

So, replacing the values, we get:

$2500=1000(1+\frac{0.07}{12})^{12t}$

Now, we need to solve for t

$\begin{gathered} \frac{2500}{1000}=(1+0.00583)^{12t} \\ 2.5=(1.00583)^{12t} \\ \log 2.5=\log (1.00583)^{12t} \\ \log 2.5=12t\log (1.00583) \\ 0.398=0.030t \\ \frac{0.398}{0.030}=t \\ 13.13=t \end{gathered}$

Therefore, it needs 13.13 years to produce $2500