Question

Mikayla opens a savings account with a principal balance of $3,000. After 5 years, she earns $450 in interest. Using the equation =rt , where = interest, = principal, = rate, and =time.

What is the interest rate on Mikayla’s account after 5 years?



*Note: Interest rate is given in percent form.

Answer 1

To solve this we are going to use the simple interest formula:
`A=P(1+rt)`
where

`A` is the final amount after
`t` years

`P` is the initial amount

`r` is the interest rate

`t` is the time in years

We know for our problem that
`P=3000`, and
`t=5`. Since she earn $450 in interest afeter 5 years,
`A=3000+450=3450`. Lets replace the values in our formula to find
`r`:

`A=P(1+rt)`

`3450=3000(1+5r)`

`1+5r= (3450)/(3000)`

`1+5r= (23)/(20)`

`5r= (23)/(20) -1`

`5r=0.15`

`r= (0.15)/(5)`

`r=0.03`
Now, the only thing left is multiply our rate by 100% to express it as a percentage:

`r=(0.03)(100)=3`%

We can conclude that the interest rate of Mikayla's savings account is 3%.