Question

5.

Find the present value of the annuity.

Amount Per Payment: $6,225

Payment at End of Each: Quarter

Number of Years: 6

Interest Rate: 8%

Compounded: Quarterly

Answer 1

To solve this we are going to use the present value of annuity formula:
`PV=P[ (1-(1+ (r)/(n))^((-kt)) )/( (r)/(n) )]`
where

`PV` is the present value

`P` is the periodic payment

`r` is the interest rate in decimal form

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

`k` is the number of payments per year

`t` is the number of years

We know for our problem that
`P=6225` and
`t=6`. To convert the interest rate to decimal form, we are going to divide it by 100%:

`r= (8)/(100)`

`r=0.08`
Since the interest is compounded quarterly, it is compounded 4 times per year, so
`n=4`. Similarly, since the payment is made at the end of each quarter, it is made 4 times per year; therefore,
`k=4`.
Lets replace the values in our formula:

`PV=P[ (1-(1+ (r)/(n))^((-kt)) )/( (r)/(n) )]`

`PV=6225[ (1-(1+ (0.08)/(4))^((-(4)(6)) )/( (0.08)/(4) )]`

`PV=117739.19`

We can conclude that the present value of the annuity is $117,739.19