Question

$1,000 is invested at a rate of 3.25%, compounded annually. Identify the compound interest function that models the situation. Then find the balance after 8 years.

Answer 1

The compounded interest function that models the situation is:
`A=P(1+ (r)/(n) )^(nt)`
where

`A` is the final amount of money after
`t` years.

`P` is the initial investment.

`r` is the interest rate in decimal form.

`n` is the number of times the interest is compounded per year.

`t` is the time in years.

We know for our problem that
`P=1000` and
`t=8`. To convert the interest rate to decimal form, we are going to divide the rate by 100%:

`r= (3.25)/(100)`

`r=0.0325`
We also know that the interest is compounded anally, so it is compounded 1 time per year; therefore,
`n=1`.
Lets replace the values in our formula to find the final amount after 8 years:

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

`A=1000(1+ (0.0325)/(1) )^((1)(8))`

`A=1000(1+ 0.0325 )^(8)`

`A=1291.58`

We can conclude that since we are dealing with compound interest we must use the function
`A=P(1+ (r)/(n) )^(nt)`. Also, after 8 years the balance in the account will be $1291.58