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28 August, 11:53

The ABC Company has contracted to make the following payments: $10 000 immediately; $1000 at the end of year 1; $1500 at the end of year 2; $2000 at the end of year 3; $2500 at the end of year 4; $3000 at the end of year 5. What fixed amount of money should the company plan to set aside each year, at 8% interest per year, compounded annually, in order to make the above payments

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  1. 28 August, 13:14
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    Company should set aside $17,680 at 8% interest per year.

    Explanation:

    The payment made in future does not have equal value as today because there is an opportunity of reinvestment of that cash flow.

    The amount of money required to make all the payment can be determined by calculating the present value of each cash payment.

    Use following present value formula

    Present value = Future value / (1 + r) ^n

    where

    r is the interest rate

    n is the number of year

    Total Amount to save for payment = Immediate payment + [ Year 1 payment / (1 + r) ^1 ] + [ Year 2 payment / (1 + r) ^2 ] + [ Year 3 payment / (1 + r) ^3 ] + [ Year 4 payment / (1 + r) ^4 ] + [ Year 5 payment / (1 + r) ^5 ]

    Total Amount to save for payment = $10,000 + [ $1,000 / (1 + 8%) ^1 ] + [ $1,500 / (1 + 8%) ^2 ] + [ $2,000 / (1 + 8%) ^3 ] + [ $2,500 / (1 + 8%) ^4 ] + [ $3,000 / (1 + 8%) ^5 ]

    Total Amount to save for payment = $10,000 + $926 + $1,286 + $1,588 + $1,838 + $2,042 = $17,680
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