Ted owns a small florist shop. Since his business is booming, his realizes he will soon need one more delivery van. He decides he will purchase a full size van versus a minivan, which he currently owns. The van he is looking to buy in 3 years will cost him $25,000. How much should he invest each quarter into an account that pays 3% per year compounded quarterly, so that he can have the desired funds in 3 years?

a) Present Value with compound interestb) Sinking Fundc) Amortizationd) Present Value of an Annuitye) Future Value with compound interestf) None of the above.

A sinking fund is an account earning compound interest into which you make periodic deposits. Suppose that the account has an annual interest rate of (r) compounded (m) times per year, so that (i=r/m) is the interest rate per compounding period. If you make a payment of PMT at the end of each period, then the future value after (t) years, or (n = mt) periods, will be

FV = [tex] PMT (〖(1+i )〗^n -1)/i [/tex]

Where FV is the amount that would be accumulated after t years

Payment Formula for a Sinking Fund

Suppose that an account has an annual rate of (r) compounded (m) times per year, so that is (i=r/m) is the interest rate per compounding period. If you want to accumulate a total of FV in the account after t years, or (n = mt) periods, by making payments of PMT at the end of each period, then each payment must be

PMT = [tex] FV ( i)/(〖(1+i)〗^n -1) [/tex]

From the question

Rate= r = 3/100 = 0.03

Number of times it was paid (compounded) in a year = m = 4 its value is Four cause the payment is made 4 times in one year i.e. Quarterly

The interest rate per compounding period = I = r/m = 0.03/4 = 0.0075

Number of times it was paid (compounded) t years n = 4 x 3 = 12

The amount that ted desires to be in that account after 3 years =FV = $25,000

So the investment that Ted needs to make Quarterly in order to get his desired amount is

= [tex]25000 × (0.0075/(〖(1+0.0075)〗^12 -1 )) [/tex]

= $2000