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Ivenika [448]
3 years ago
6

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

Mathematics
1 answer:
mylen [45]3 years ago
8 0

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

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