suppose that you deposit 700 dollars each month into a savings account that earns 2 percent interest per…

Answer:

$87347.43$

Explanation:

Step1: Identify the relevant formula

The future - value of an ordinary annuity formula is $F = A\times\frac{(1 + r)^{n}-1}{r}$, where $A$ is the annuity payment, $r$ is the interest rate per period, and $n$ is the number of periods.

Step2: Calculate the interest rate per period

The annual interest rate $i = 2%=0.02$. Since it is compounded monthly, the interest rate per month $r=\frac{0.02}{12}$.

Step3: Determine the number of periods

The time is 9 years, and since there are 12 months in a year, the number of periods $n = 9\times12=108$. The annuity payment $A = 700$.

Step4: Substitute values into the formula

$F=700\times\frac{(1+\frac{0.02}{12})^{108}-1}{\frac{0.02}{12}}$. First, calculate $(1+\frac{0.02}{12})^{108}$. Let $x=\frac{0.02}{12}\approx0.001667$, then $(1 + x)^{108}=(1 + 0.001667)^{108}$. Using the formula $(a + b)^n=\sum_{k = 0}^{n}\binom{n}{k}a^{n - k}b^{k}$, or simply using a calculator, $(1+0.001667)^{108}\approx1.190677$. Then, $(1+\frac{0.02}{12})^{108}-1\approx1.190677 - 1=0.190677$. $\frac{(1+\frac{0.02}{12})^{108}-1}{\frac{0.02}{12}}=\frac{0.190677}{\frac{0.02}{12}}=\frac{0.190677\times12}{0.02}=114.4062$. Finally, $F = 700\times114.4062=87347.43$.