4. James and Terry open a savings account that has a 2.75% annual interest rate, compounded monthly. They
1 answer:
$ 159,744.59 will be in the account after 20 years.
Answer: Option A
<u>Step-by-step explanation:</u>
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)](https://tex.z-dn.net/?f=%5Ctext%20%7BFuture%20value%7D%3Dp%20%5Ctimes%5Cleft%28%5Cfrac%7B%5Cleft%281%2B%5Cfrac%7Br%7D%7Bn%7D%5Cright%29%5E%7Bn%20t%7D-1%7D%7B%5Cfrac%7Br%7D%7Bn%7D%7D%5Cright%29)
Here
p : amount deposit monthly =$500
r : rate of interest =
= 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)](https://tex.z-dn.net/?f=%5Ctext%20%7B%20Future%20value%20%7D%3D500%20%5Ctimes%5Cleft%28%5Cfrac%7B%5Cleft%281%2B%5Cfrac%7B0.0275%7D%7B12%7D%5Cright%29%5E%7B240%7D-1%7D%7B%5Cfrac%7B0.0275%7D%7B12%7D%7D%5Cright%29)
![\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)](https://tex.z-dn.net/?f=%5Ctext%20%7BFuture%20value%7D%3D500%20%5Ctimes%5Cleft%28%5Cfrac%7B%281%2B0.002291%29%5E%7B240%7D-1%7D%7B0.002291%7D%5Cright%29%3D500%20%5Ctimes%5Cleft%28%5Cfrac%7B%281.732%29-1%7D%7B0.002291%7D%5Cright%29)
![\text { Future value }=500 \times\left(\frac{0.732}{0.002291}\right)=500 \times 319.511=\$ 159,744.99](https://tex.z-dn.net/?f=%5Ctext%20%7B%20Future%20value%20%7D%3D500%20%5Ctimes%5Cleft%28%5Cfrac%7B0.732%7D%7B0.002291%7D%5Cright%29%3D500%20%5Ctimes%20319.511%3D%5C%24%20159%2C744.99)
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