(3) Suppose $40,000 was invested on January 1, 1980 at an annual effective in- terest rate of 7% in order to provide an annual (calendar-year) scholarship of $5,000 each year forever, the scholarships paid out each January 1. (b) What smaller scholarship can be awarded the year prior to the first $5,000 scholarship?
We have to calculate the present value of perpetual annuity due. This value will be equal to the future value compounded of the initial investment $40000 by "n" periods. We have to find the value of n first. Remember, the first annuity is paid on the 1st of January every year so if the value of n is a fraction, then we will have to take the next integer value as the day of the 1st annuity payment. Calculate the future value of the $40000 compounded to the period of the integer value and then subtract the value of the perpetuity from it to get to the smaller scholarship that can be awarded to the first scholarship. Please refer to the below for all the excel calculations.
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