Question

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. $159,744.59 B. $48,407.45 C. $330,600.15 D. $580,894.18

Answer 1

Answer:

Option A is the answer(here the answer is calculated taking the whole value, without approximating it to a nearest value)

Step-by-step explanation:

Annual interest rate is 2.75%. Hence, the monthly interest rate is $\frac{2.75}{12}$

The amount will be compounded $(20\times12) = 240$ times.

Every month they deposits $500.

In the first month that deposited $500 will be compounded 240 times.

It will be $500\times [1 + \frac{2.75}{1200} ]^{240}$

In the second month $500 will be deposited again, this time it will be compounded 239 times.

It will give $500\times [1 + \frac{2.75}{1200} ]^{239}$

Hence, the total after 20 years will be $500\times [1 + \frac{2.75}{1200} ]^{240} + 500\times [1 + \frac{2.75}{1200} ]^{239} + ........+ 500\times [1 + \frac{2.75}{1200} ]^{1} = 160110.6741$