$A is invested today into a scholarship fund earning j₁ = 8%.The first scholarship (paid 1 year from now)is $1000 and each succeeding scholarship is $2000 a year.What is A? (Answer to nearest dollar)

Question

Quizplus · Accepted Answer

Let A be the initial investment amount.
After one year, the investment will grow to A(1+0.08) = 1.08A.
The value of the scholarship at time n is 1000 + 2000(n-1) = 2000n - 1000.
To ensure that there is enough money to pay for all scholarships, we can set up an equation:

1.08A = 2000 + (2000+1000)/1.08 + (2000+3000)/1.08^2 + ... + (2000+1000(n-2))/1.08^(n-1)

Using the formula for the sum of an infinite geometric series, we can simplify this to:

1.08A = 2000 + 3000/0.08 = 61000

Solving for A, we get:

A = 61000/1.08 = $24,074.07

Rounding to the nearest dollar, we get A = $24,074, which corresponds to answer choice B.

$A Is Invested Today into a Scholarship Fund Earning J1

$A Is Invested Today into a Scholarship Fund Earning J₁