A scholarship fund has $50,000 in it today and it earns interest at j₂ = 8%.The fund is to pay out a perpetuity of $R every 6-months,with the first payment to be made 1 year from today.What is R? (Answer to nearest dollar)

Question

Quizplus · Accepted Answer

To calculate the perpetuity payment that the scholarship fund can afford to pay out every 6 months, we can use the formula:

P = A / (1 + r)^n

Where:
P = payment amount
A = initial amount of the fund ($50,000)
r = interest rate (8% or 0.08)
n = number of payment periods in a year (2)

We can rearrange this formula to solve for the payment amount (P):

P = A * r / (1 - (1 + r)^-n)

Substituting in the values:

P = $50,000 * 0.08 / (1 - (1 + 0.08)^-2)
P = $4160

This is the total payment amount that the scholarship fund can afford to make every year. To find the payment amount every 6 months, we divide by 2:

P/2 = $2080

Therefore, the answer is B) $2080.

A Scholarship Fund Has $50,000 in It Today and It