Question

Find the future value of an annuity due of $400 each quarter for 4 1 2 years at 13%, compounded quarterly. (Round your answer to the nearest cent.)

Answer 1

$9891.23

Explanation:

The formula for future value of annuity due is:

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

Where,

• FV is the future value of the annuity (what we need to find)
• P is the periodic payment (here it is $400)
• r is the interest rate per period (here 13% yearly interest is actually
  `(13)/(4)=3.25` percent per period(quarter))
• n is the number of periods (here the annuity is for
  `4(1)/(2)` years, which is
  `4(1)/(2)*4=18` periods, since quarterly and there are 4 quarters in 1 year)

Substituting all those values in the equation we get:

`FV=400[((1+0.0325)^(18)-1)/(0.0325)]*(1+0.0325)\\=400[23.9497]*(1.0325)\\=9891.23`

Hence, the future value of the annuity due is $9891.23