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.

The type of the problem described above is a Sinking Fund

Option B

Step-by-step explanation:

In order to understand the solution to this question we have to be familiar with these concepts  

Sinking Fund

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 =

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 =

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  

               =

                = $2000  

the answer is y = 11.54

hope this : )

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