Question

Carly opened a savings account and deposited 500.00 the account earns 1%interest compounded monthly if she wants to use the money to buy a new bicycle in 3 years how much will she be able to spend on the bike

Answer 1

The information we have is:

Principal or amount saved:

`P=500`

Interest rate:

`r=1\text{ percent}`

We will need r in decimal, so we divide the percentage by 100:

`r=0.01`

The number of years:

`t=3`

We will also need the number of times that the interest is compounded on that time. Since it is compounded monthly, the amount n, which is the number of times that it is compounded in 1 year is

`n=12`

That is because 1 year has 12 months.

Now that we have all of the information we need, we can use the compounded interest formula to find the amount A that she will have after 3 years:

`A=P(1+(r)/(n))^(nt)`

Substituting all of our values:

`A=500(1+(0.01)/(12))^(12*3)`

Solving the operations, we get:

`A=500(1+(0.01)/(12))^(36)`
`\begin{gathered} A=500(1+0.00083)^(36) \\ \end{gathered}`
`A=500(1.00083)^(36)`
`\begin{gathered} A=500(1+0.00083)^(36) \\ A=500(1.03044) \\ A=515.22 \end{gathered}`

Answer:

She will have $515.22 to spend on the bike