Question

Consider the following scenario: A company is planning to purchase a large and expensive asset six years from now (at the end of the year). They plan to deposit $9,575 into an account at the end of each quarter for the next six years to fund this purchase. The account earns 9% interest compounded semi-annually (i.e. two times per year). Which of the following best represents how much will the company have saved at the end of this six year period?

Answer 1

Solution :-

Interest Rate ( Compounded Semiannually ) = 9%

Therefore Semiannual Rate = 9% / 2 = 4.5%

Now Interest Rate per Quarter = ( 1 + 0.045 )^1/2 - 1 = 0.02225 = 2.225%

Amount Deposited at the end of each quarter = $9,575

Total Quarterly Deposits in 6 Years = 6 * 4 = 24

Now The Amount at the end of 6 Years =

= $9,575 * FVAF ( 2.225% , 24 )

= $9,575 * [ ( 1 + 0.02225 )²⁴ - 1 ] / 0.02225

= $430,290.37 * [ 1.6959 - 1 ]

= $299,430.84

The amount that company have saved at the end of this six year period = $299,430.84

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