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.)
Question
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.)
Solution
The value of a growing perpetuity can be calculated using the formula:
PV = D / (r - g)
where: PV = present value D = dividend (or cash flow) expected at the end of the first period r = discount rate g = growth rate
In this case, the first payment (D) is $3,167, the interest rate (r) is 9% or 0.09, and the growth rate (g) is 3% or 0.03.
Substituting these values into the formula gives:
PV = 3167 / (0.09 - 0.03)
Solving this equation gives:
PV = 3167 / 0.06
PV = $52,783.33
So, the value of the bequest today is closest to $52,783.33.
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