2. if you saved $700 a month (the average car payment) for 40 years with an initial deposit of $700, how…

Explanation:

Step1: Convert years to months

The number of months $n = 40\times12=480$ months. The annual interest rate $r = 10%=0.1$, so the monthly interest rate $i=\frac{0.1}{12}$. The initial - deposit $P_0 = 700$ and the monthly deposit $P = 700$.

Step2: Use the future - value of an ordinary annuity formula and add the future value of the initial deposit

The future - value of an ordinary annuity formula is $FVA=P\times\frac{(1 + i)^n-1}{i}$, and the future value of the initial deposit is $P_0\times(1 + i)^n$. The future - value of the annuity: [ \begin{align*} FVA&=700\times\frac{(1+\frac{0.1}{12})^{480}-1}{\frac{0.1}{12}}\ \end{align*} ] Let $x=(1+\frac{0.1}{12})^{480}$. First, calculate $(1+\frac{0.1}{12})\approx1.008333$. Then $x = 1.008333^{480}$. Using a calculator, $1.008333^{480}\approx52.9871$. [ \begin{align*} FVA&=700\times\frac{52.9871 - 1}{\frac{0.1}{12}}\ &=700\times\frac{51.9871}{\frac{0.1}{12}}\ &=700\times51.9871\times120\ &=700\times6238.452\ & = 4366916.4 \end{align*} ] The future value of the initial deposit $P_0\times(1 + i)^n=700\times52.9871 = 37090.97$. The total future value $F = FVA+P_0\times(1 + i)^n$. [ \begin{align*} F&=4366916.4+37090.97\ &=4404007.37 \end{align*} ]

Answer:

$$4404007.37$