Question

Suppose $40,000 was invested on January 1, 1980 at an annual effective interest 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.
(a) In what 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

Explanation:

a). This can be expressed as follows;

I=PRT

where;

I=Interest amount

P=Initial value of investment

R=Annual interest rate

T=number of years the money is invested for

In our case;

I= $5,000

P=$40,000

R=7%=7/100=0.07

T=t

Replacing;

5,000=40,000×0.07×t

5,000=2,800 t

t=5,000/2,800

t=1.786 years which will be 2 years since although the first amount will be in 1.7 years, the interest has to be paid on January 1 of the next year

1980+2=1982

The first $5,000 will be paid on January 1, 1982

b). What to receive after 1 year

I=PRT

where;

P=$40,000

R=7%=7/100=0.07

T=1

I=(40,000×0.07×1)=2,800

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