Question

Your grandfather wants to establish a scholarship in his father’s name at a local university and has stipulated that you will administer it. As you’ve committed to fund a $10,000 scholarship every year beginning one year from tomorrow, you’ll want to set aside the money for the scholarship immediately. At tomorrow’s meeting with your grandfather and the bank’s representative, you will need to deposit____________ (rounded to the nearest whole dollar) so that you can fund the scholarship forever—assuming that the account will earn 6.00% per annum every year.
a. $111,111
b. $88,889
c. $100,000
d. $133,333

The bank representative just reported that he misquoted the available interest rate on the scholarship’s account. Your account should earn 4.75%. The amount of your required deposit should be revised to______ .

a. $60,715
b. $53,572
c. $71,429
d. $67,858

This suggests there is________ relationship between the interest rate earned on the account and the present value of the perpetuity.

a. A direct
b. An inverse

Answer 1

Answer:

the answer for the first question is $166667.

the answer for the second question is $210526

the answer for the third question is An inverse.

Explanation:

given information that i will invest in a $10000 scholarship that will pay forever.

the interest rate charged is 6.00% per annum therefore this is a perpetuity present value problem where there is streams of income forever therefore we use the formula :

Pv of perpetuity= Cf/r

where Cr is the cash flows payed by the single investment forever in this case $10000 then r is the interest rate of the investment amount which is 6% in this case.

Pv of Perpetuity= $10000/6%

                           =$166667 therefore i must invest this amount to get the scholarship running with streams of $10000 forever.

in the second problem if now the interest rate is changed from 6% to 4.75% then the amount to be invested would be :

Pv of perpetuity = $10000/4.75%

                              =$210526 therefore this is the amount to be invested for a forever $10000 stream of incomes for a scholarship.

the relationship is indirect cause as the interest rate decreases the present value of the perpetuity that must be invested increases.