Question

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

Answer 1

The value of annuity is
`P_v = \$ 7929.9`

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 + (r)/(n) )^(-t * n) ] * [((1 + (r)/(n) ))/( (r)/(n) ) ]` (reference EDUCBA website)

substituting values

`P_v = 250 * [1 - (1 + (0.05)/(4) )^(-10 * 4) ] * [((1 + (0.05)/(4) ))/( (0.08)/(4) ) ]`

`P_v = 250 * [1 - (1.0125 )^(-40) ] * [((1.0125 ))/(0.0125) ]`

`P_v = 250 * [0.3916 ] * [((1.0125))/(0.0125) ]`

`P_v = \$ 7929.9`