Question

4. James and Terry open a savings account that has a 2.75% annual interest rate, compounded monthly. They
deposit $500 into the account each month. How much will be in the account after 20 years?
a. S159,744.59
b. S48,407.45
c. $580,894.18
d. $330,600.15

Answer 1

$ 159,744.59 will be in the account after 20 years.

Answer: Option A

Step-by-step explanation:

Need to find out the amount present in the account after 20 years. The formula to find out the future value is,

          $\text {Future value}=p \times\left(\frac{\left(1+\frac{r}{n}\right)^{n t}-1}{\frac{r}{n}}\right)$

Here  

p : amount deposit monthly =$500

r : rate of interest  = $\frac{2.75}{100}$ = 0.0275

n : 12(compound monthly)

t : time =20

By substituting all the given datas in the above equation, we get

    $\text { Future value }=500 \times\left(\frac{\left(1+\frac{0.0275}{12}\right)^{240}-1}{\frac{0.0275}{12}}\right)$

    $\text {Future value}=500 \times\left(\frac{(1+0.002291)^{240}-1}{0.002291}\right)=500 \times\left(\frac{(1.732)-1}{0.002291}\right)$

   $\text { Future value }=500 \times\left(\frac{0.732}{0.002291}\right)=500 \times 319.511=\ 159,744.99$