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

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 *\left((\left(1+(r)/(n)\right)^(n t)-1)/((r)/(n))\right)`

Here

p : amount deposit monthly =$500

r : rate of interest =
`(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 *\left((\left(1+(0.0275)/(12)\right)^(240)-1)/((0.0275)/(12))\right)`

`\text {Future value}=500 *\left(((1+0.002291)^(240)-1)/(0.002291)\right)=500 *\left(((1.732)-1)/(0.002291)\right)`

`\text { Future value }=500 *\left((0.732)/(0.002291)\right)=500 * 319.511=\$ 159,744.99`