Savings

Suppose on your 21st birthday you begin making monthly payments of $500 into an account that pays 8% compounded monthly. If you continue the payments until your 51st birthday (30 years), How much money is in your account? How much of it is interesting? Show solution. (Future value with regular contributions, future value of a series)

Correct answer:

x =  745179.7243
i =  565179.7243

Step-by-step explanation:

$$\begin{gathered} PMT=500 \\ r=8\%=\frac{8}{100}=\frac{2}{25}=0.08 \\ n=12 \\ t=30 \\ q=r/n=\frac{2}{25}/12=\frac{2}{25\cdot 12}=\frac{2}{300}=\frac{1}{150}\doteq 0.0067 \\ m=n\cdot t=12\cdot 30=360 \\ x=PMT\cdot \frac{(1+q{)}^m-1}{q}=500\cdot \frac{(1+\frac{1}{150}{)}^{360}-1}{\frac{1}{150}}=745179.7243\doteq 7.452\cdot 10^5 \end{gathered}$$

$i=x-m\cdot PMT=\frac{116248037}{156}-360\cdot 500=565179.7243\doteq 5.652\cdot 10^5$

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