Question

Find the value of annuity if the periodic deposit is $250 at 5% compounded quarterly for 10 years

Answer 1

Answer:

The value of  annuity is  $P_v = \ 7929.9$

Step-by-step explanation:

From the question we are told that

    The periodic payment is  $P = \ 250$

     The  interest rate  is   $r = 5\% = 0.05$

     Frequency at which it occurs in a year is  n = 4 (quarterly )

      The number of years is  $t = 10 \ years$

The  value of the annuity is mathematically represented as

             $P_v = P * [1 - (1 + \frac{r}{n} )^{-t * n} ] * [\frac{(1 + \frac{r}{n} )}{ \frac{r}{n} } ]$ (reference EDUCBA website)

 substituting values

             $P_v = 250 * [1 - (1 + \frac{0.05}{4} )^{-10 * 4} ] * [\frac{(1 + \frac{0.05}{4} )}{ \frac{0.08}{4} } ]$

             $P_v = 250 * [1 - (1.0125 )^{-40} ] * [\frac{(1.0125 )}{0.0125} ]$

             $P_v = 250 * [0.3916 ] * [\frac{(1.0125)}{0.0125} ]$

            $P_v = \ 7929.9$