Question

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 I.
(a) In that year can the first $5,000 scholarship be made?
(b) What smaller scholarship can be awarded the year prior to the first $5,000
scholarship?​

Answer 1

Answer:a). The first $5,000 will be paid on January 1, 1982

b). The smaller scholarship that will be received=$2,800

Step-by-step explanation:

First part is good. Since we are dealing with annuities-due you need to divide the contribution of $5000 / d where d = i/1+i = .0654

Now, to find the smaller payment 1 year prior to the first $5000 the way I did it was,

FV = 40,000 (1.07)^9 = $73,538.37

Now, we know in order for the scholarship to be available, the funds need to increase up to $76,428.57.

So at year 9, which is .57 years away before the funds reach maturity is

76,428.57 - 73,538.37 = 2,890.20

Now, that value represents the .57 or in this case, we want to be exact so, .56976171 years left until maturity which means that at the current moment

C - C(.56976171) = 5000 - 2890.20 = $2,109.80 has already been earned and can be paid on January 1, 1989.

Answer 2

Answer:

(B). $5,000 This is correct answer.