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Jasmine wants to fund a scholarship in honour of her parents that will pay $15 000 per year to a deserving student, starting next year. She wants the annual amount paid to the student to grow by 2% per year to keep up with student fee increases. Given that the interest rate she can earn on her investment is 6%, how much does she need to fund this perpetuity?

Question

Jasmine wants to fund a scholarship in honour of her parents that will pay $15 000 per year to a deserving student, starting next year. She wants the annual amount paid to the student to grow by 2% per year to keep up with student fee increases. Given that the interest rate she can earn on her investment is 6%, how much does she need to fund this perpetuity?

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Solution

To solve this problem, we need to use the formula for the present value of a growing perpetuity. The formula is:

PV = D / (r - g)

where:

  • PV is the present value, or the amount Jasmine needs to fund the perpetuity.
  • D is the first payment, or $15,000.
  • r is the interest rate, or 6% (0.06 in decimal form).
  • g is the growth rate, or 2% (0.02 in decimal form).

Substituting the given values into the formula, we get:

PV = 15000 / (0.06 - 0.02)

Solving this equation gives us the amount Jasmine needs to fund the perpetuity.

This problem has been solved

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