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

Step-by-step explanation:

For compound interest, we have the following equation

`A=P(1+(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+(0.07)/(12))^(12t)`

Now, we need to solve for t

`\begin{gathered} (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 \\ (0.398)/(0.030)=t \\ 13.13=t \end{gathered}`

Therefore, it needs 13.13 years to produce $2500