Mathematics: 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?

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Suppose you want your daughters college fund to

leigha03

21.01.2022

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

Step-by-step 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

$A=\frac{P_{Mt}[(1+\frac{r}{n})^{nt}-1]}{\frac rn}$

A = amount=$125,000

P= principal =?

r= rate of interest= 7.8%=0.078

n=12 [compounded monthly]

t= 14 years

$\therefore 125,000=\frac{P_{Mt}[(1+\frac{0.078}{12})^{12\times14}-1]}{\frac{0.078}{12}}$

$\Rightarrow 125,000=\frac{P_{Mt}[(1.0065)^{168}-1]}{0.0065}$

$\Rightarrow P=\frac{125,000}{303.03}$

⇒P=$412.50(approx)

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

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