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

Hence,

`\begin{gathered} =(100((1+(7)/(1200))^(360)-1))/((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 }*\text{ 30 }*12\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