Question

Yvonne put $4000 in a savings account. At the end of three years, the account had earned $960 in simple interest. A. How much does she have in her own account at the end of three years? B. What annual simple interest rate did the account grow? Show your work. C. How many more dollars would she have in her account if the interest rate were 1% greater? Show your work.

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 in decimal form

`t` is the time in years

A. We now form our problem that her initial savings were $4000. Since she earned $960 in interest after 3 years, her final amount will be his initial savings plus the interest hat she earned:

`A=4000+960`

`A=4960`
We can conclude that she will have $4960 in her account at the end of three years.

B. We know for our problem that
`P=4000`, and
`t=3`. We also know that the account earned $960 in interest, so
`A=4000+960=4960`. Let
`x` represent the interest rate; since the interest rate should be in decimal form,
`r= (x)/(100) =0.01x`. Lets replace all the values in our formula to find
`x`:

`4960=4000[1+(0.01x)(3)]`

`4960=4000(1+0.03x)`

`4960=4000+120x`

`120x=960`

`x= (960)/(120)`

`x=8`
We can conclude that the account growth by an annual simple interest rate of 8%

C. if the interest rate were 1% greater, our new
`r` is going to be
`r=8+9`. But remember that the interest rate should by in decimal form, so we are going to divide 9% by 100%:

`r= (9)/(100)`

`r=0.09`
We also know that the conditions are the same as before, so
`P=4000` and
`t=3`. Lets replace all our values in our formula to find
`A`:

`A=4000[1+(0.09)(3)]`

`A=4000(1+0.27)`

`A=4000(1.27)`

`A=5080`
We can conclude that she will have
`5080-4960=120` $ more in her account if the interest rate were 1% greater.