Question

You deposit $100 each month into an account earning 7% interest compounded monthly

Answer 1

Step 1

Given;

$\begin{gathered} A\text{ deposit of \ 100 each month} \\ 7\text{\% interest com}pounded\text{ }monthly \end{gathered}$

Step 2

State the formula to simplify the problem

$=A(\frac{(1+i)^n-1}{i})$$\begin{gathered} A=\text{ \ 100} \\ i\text{ = }\frac{0.07}{12}=\frac{7}{1200} \\ n=\text{ 30 years}=\text{ 30 x }12=\text{ 360 months} \end{gathered}$

Hence,

$\begin{gathered} =\frac{100((1+\frac{7}{1200})^{360}-1)}{\frac{7}{1200}} \\ =\text{\ }121997.0966 \\ \approx\text{\ }121997.1 \end{gathered}$

Hence, the account will have $121997.1 in 30 years

Step 3

Find how much total money will be put in the account.

$=\text{ 100 }\times\text{ 30 }\times12\text{ =\ }36000$

The total amount of money that will be put into the account = $36000

Step 4

Find out how much total interest you will earn

$\begin{gathered} Interest\text{ = amount in 30 years - total money} \\ \text{Interest = }121997.1-36000 \\ \text{Interest = \ }85997.1 \end{gathered}$

Total interest you will earn = $85997.1