Question

2.

Find the amount of the annuity.

Amount of Each Deposit: $295

Deposited: Quarterly

Rate per Year: 10%

Number of Years: 6

Type of Annuity: Due


$9,671.28

$9,542.97

$10,076.54

$9,781.54

Answer 1

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

`FV` is the future 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=295` and
`t=6`. To convert the interest rate to decimal for, we are going to divide the rate by 100%:

`r= (10)/(100)`

`r=0.1`
Since the payment is made quarterly, it is made 4 times per year; therefore,
`k=4`.
Since the type of the annuity is due, payments are made at the beginning of each period, and we know that we have 4 periods, so
`n=4`.
Lets replace those values in our formula:


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

`FV=(1+ (0.1)/(4) )*295[ ((1+ (0.1)/(4) )^((4)(6)) -1)/( (0.1)/(4) ) ]`

`FV=9781.54`

We can conclude that the amount of the annuity after 10 years is $9,781.54