Question

Clarissa wants to fund a growing perpetuity that will pay $10,000 per year to a local museum, starting next year. She wants the annual amount paid to the museum to grow by 5% per year. Given that the interest rate is 9%, how much does she need to fund this perpetuity?

Answer 1

Answer:

$250,000

Explanation:

Perpetuity is a type of payment that has no end. It starts on a particular date and continues endlessly.

Given:

Amount paid per year = $10,000

Annual Growth Rate = 5%

Interest Rate = 9%

$Perpetuity = Amount paid/(Interest rate-Growth rate)\\Perpetuity = 10,000/(9/100-5/100)\\ Perpetuity= 10,000/0.04\\Perpetuity =250,000$

Clarissa need $250,000

Answer 2

Answer:

$250,000

Explanation:

In finance, perpetuity refers to an annual payment that does not ever end. This stream of cash is meant to continue forever. Perpetuities still exist, but are very rare. In this case, Clarissa wants to fund a perpetuity that will pay $10,000 per year, grow by 5%, and have an interest rate of 9%.

The formula for this would be:

PV0= 10000 / (0.09 - 0.05) =

PV0= 10000 / 0.04 =

PV0= 250,000