Question

Question 1 (4 points) Income from the recycling paper and cardboard at Hamden recycling center has averaged $9,000 per quarter for 5 years. What is the future worth of the income at year 5 at an interest rate of 4%, compounded semiannually? a) Assume that interperiod cash flows earn prorated compound interest. b) Assume there is no interperiod compounding. 1

Answer 1

a)

Quarterly income = $9,000

Interest rate = 4% per year compounded semiannually

Since, interest is compounded semi annually, interest rate divided by 4 and time period has to be multiplied by 4

Adjusted interest rate (i) = 4%/4 = 1%

Adjusted time period (n) = 5 years *4 = 40

Now we calculate the Future worth now -

F = A (F/A, i, n)

= $9,000 (F/A, 1%,40)

= $9,000 * (48.886)

= $439,974

Therefore the Future worth is $439,974

b)

Quarterly income = $9,000

So, Semiannual income = $9,000 * 2 = $18,000

Interest rate = 4% per year compounded semiannually

Since, interest is compounded semi annually, interest rate divided by 2 and time period has to be multiplied by 2.

Adjusted interest rate (i) = 4/2 = 2%

Adjusted time period (n) = 5 years *2  = 10

Now we calculate the Future worth now -

F = A (F/A, i, n)

= $18,000 (F/A, 2%,10)

= $18,000 * (10.950)

= $197,100.00

Therefore the Future worth is $197,100

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