Question

How much will deposits of $900 made at the end of each 6 months amount to after 11 years if interest is 5.4% compounded annually?

Answer 1

Ordinary Annuity

When the deposits are made at end of the every half year then it is known as ordinary annuity

We can use the formula for finding the periodic deposit value as below

A = R x [ ( 1 + (i/n) )^nt-1 ] / ( i/n )

Here A = future value = $?

        R = Cash flow per period = $900

        r = rate of interest = 5.4% = 5.4/100 = 0.054

                n = compounding frequency is half yearly so n= 2

       t = Number of years = 11 years

FV = 900 x [ ( 1 + (0.054/2 ))²⁽¹¹⁾ – 1 ] / (0.054/2)]

FV = 900 x [ ( 1 + (0.027))⁽²²⁾ – 1 ] / (0.027)]

FV = 900 x [ ( 1.027))⁽²²⁾ – 1 ] / (0.027)]

FV = 900 x [ 1.797– 1 ] / (0.027)]

FV = 900 x [ 0.797] / (0.027)]

FV = 900 x [ 29.5185]

FV = 26566.65

So the future value = $26566.65