Question

Suppose you want your daughters college fund to contain $125,000 after 14 years. If you can get 7.8% compounded monthly, how much should you deposit at the end of each month?

Answer 1

Therefore I should deposit $412.50 at the end of each month.

Explanation:

Given that, I want my daughters college fund to contain$125,000 after 14 year. The rate of interest 7.8% compounded monthly.

To find the the deposit, we use the following formula

`A=(P_(Mt)[(1+(r)/(n))^(nt)-1])/(\frac rn)`

A = amount=$125,000

P= principal =?

r= rate of interest= 7.8%=0.078

n=12 [compounded monthly]

t= 14 years

`\therefore 125,000=(P_(Mt)[(1+(0.078)/(12))^(12*14)-1])/((0.078)/(12))`

`\Rightarrow 125,000=(P_(Mt)[(1.0065)^(168)-1])/(0.0065)`

`\Rightarrow P=(125,000)/(303.03)`

⇒P=$412.50(approx)

Therefore I should deposit $412.50 at the end of each month.