Knowee
Questions
Features
Study Tools

Martin wants to provide money in his will for an annual bequest to whichever of his living relatives is oldest. That bequest will provide $1 000 in the first year, and will grow by 7% per year, forever. If the interest rate is 11%, how much must Martin provide to fund this bequest?

Question

Martin wants to provide money in his will for an annual bequest to whichever of his living relatives is oldest. That bequest will provide $1 000 in the first year, and will grow by 7% per year, forever. If the interest rate is 11%, how much must Martin provide to fund this bequest?

🧐 Not the exact question you are looking for?Go ask a question

Solution

To solve this problem, we need to understand the concept of a growing perpetuity. A growing perpetuity is a series of periodic payments that grow at a proportionate rate and are received for an infinite amount of time.

The formula for the present value of a growing perpetuity is:

PV = D / (r - g)

where:

  • PV is the present value (the amount Martin must provide to fund the bequest)
  • D is the cash inflow (the bequest) in the first period
  • r is the discount rate (the interest rate)
  • g is the growth rate

In this case:

  • D = $1,000
  • r = 11% or 0.11
  • g = 7% or 0.07

Substituting these values into the formula, we get:

PV = $1,000 / (0.11 - 0.07)

Solving this equation will give us the amount Martin must provide to fund the bequest.

This problem has been solved

Similar Questions

A rich relative has bequeathed you a growing perpetuity. The first payment will occur in a year and will be $2 000. Each year after​ that, you will receive a payment on the anniversary of the last payment that isnbsp 5% larger than the last payment. This pattern of payments will go on forever. If the interest rate is 16% per​ year, a.  What is​ today's value of the​ bequest? b.  What is the value of the bequest immediately after the first payment is​ made?

A father left a will of Rs. 85,000 to be divided between his two sons aged 10 years and 12 years such that they may get equal amount when each attains the age of 18 years. If the money is invested at 10% p.a. simple interest, then find how much (in Rs.) would the son aged 10 years gets at the time of the execution of the will.1)  30,0002)  40,0003)  45,0004)  48,000

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?

Your aunt has gifted you a growing perpetuity. The first payment will occur in a year and will be $3,167. Each year after that, on the anniversary of the last payment, you will receive a payment that is 3% larger than the last payment. This pattern of payments will go on forever. If the interest rate is 9% per year, the value of the bequest today is closest to? (Round your answer in dollars to 2 decimal places, e.g. put 1204.42 if your answer is 1204.4243.)

You have just deposited $7,000 into an account that promises to pay you an annual interest rate of 5.7 percent each year for the next 8 years. You will leave the money invested in the account and 20 years from today, you need to have $19,100 in the account. What annual interest rate must you earn over the last 12 years to accomplish this goal?Multiple Choice4.78%4.41%4.35%5.38%3.82%

1/3

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.