The meaning of Interest Rates - Perpetuities and Annuities

5 important questions on The meaning of Interest Rates - Perpetuities and Annuities

What is a perpetuity?

When a constant cash flow will occur at regular intervals forever

The university wants to budget $ 30 000 per year forever for graduation party. It earns 8ù per year on its investments and the first party is in one year time, how much will you need to donate now?

PV = C/r = $30.000/0.08 = $ 375 000 today

What do you choose: a) take 30 payments of $ 1 million per year (starting today) or b) $ 15 paid today (interest rate 8%)

a) PV (annuity) = $11.16 million+ $1 million
b) if you use $1 million today and invest $14 million with 8% interest you earn 1.12 million per year in perpetuity
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What is the formula of growing perpetuity?

PV(growing perpetuity) = C/(r-g)

If you save $10 000 and you increase these savings by 5% per year. How much will be saved 30 years from now with 10% on the savings?

PV = $ 150 436
in 30 years = $ 2.625 million

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