Question

Find the value of annuity if the periodic deposit is $1500 at 8% compounded semiannually for 22 years

Answer 1

Answer:

The value of  annuity is $P_v = \ 32058$

Step-by-step explanation:

From the question we are told that

    The periodic payment is  $P = \ 1500$

     The  interest rate  is   $r = 8\% = 0.08$

     Frequency at which it occurs in a year is  n = 2 (semi-annually )

      The number of years is  $t = 22 \ years$

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

             $P_v = 1500 * [1 - (1 + \frac{0.08}{2} )^{-22 * 2} ] * [\frac{(1 + \frac{0.08}{2} )}{ \frac{0.08}{2} } ]$

             $P_v = 1500 * [1 - (1.04 )^{-44} ] * [\frac{(1.04 )}{0.04} ]$

             $P_v = 1500 * [1 - 0.178 ] * [\frac{(1.04 )}{0.04} ]$

            $P_v = \ 32058$