Question

Find the amount of the payment to me made into a sinking fund so that enough will be present to accumulate the following amount. Payments are made at the end of $95,000; money earns 4% compounded semiannually for 2 and a half years.

the payment size is $

(do not round until the final answer. then round to the nearest cent)

Answer 1

Ordinary Annuity

If the monthly payment made at the end of the semi annually then we can use the ordinary annuity formula

We can use the formula for finding the future value as below

FV = P x [ ( 1 + (r/n) )^nt-1 ] / ( r/n )

Here FV =  future value = $95000

        P = Cash flow per period  = $?

        r = rate of interest = 4% = 4/100 = 0.04

                n = compounding frequency is semi annually so n= 2

       t = Number of years  = 2.5 years

95000 = P x [ ( 1 + (0.04/2 ))^2(2.5) – 1 ] / (0.04/2)]

95000 = P x [ ( 1 + (0.02))⁵ – 1 ] / (0.02)]

95000 = P x [ ( 1.02)⁵ – 1 ] / (0.02)]

95000 = P x [ 1.10408 – 1 ] / (0.02)]

95000 = P x [ 0.10408] / (0.02)]

95000 = P x [5.20404]

P = 95000 / 5.20404

P = 18255.048 ~ 18255.05

So required semi annual payment = $18255.05