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An annuity pays out $5000 at the beginning of each year in perpetuity. If the interest is 5% compounded annually, find: a/ The present value of the whole annuity; b/ The present value of the annuity for payments received, starting from the end of 20ᵗʰ year.

User Blo
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Final answer:

The present value of the whole annuity is $100,000. The present value of the annuity for payments received, starting from the end of the 20th year, is $163,931.44.

Step-by-step explanation:

To find the present value of an annuity, we can use the formula:



Present Value = Payment / Interest Rate



a/ The present value of the whole annuity is calculated by dividing the annual payment of $5000 by the interest rate of 5%:



Present Value = $5000 / 0.05 = $100,000



b/ To find the present value of the annuity for payments received, starting from the end of the 20th year, we need to calculate the present value of the first 19 years of payments. Then, we can calculate the present value of the remaining perpetuity:



Present Value of the first 19 years = $5000 * (1 - (1 + 0.05)^{-19}) / 0.05 = $63,931.44



Present Value of the perpetuity = $5000 / 0.05 = $100,000



Total Present Value = Present Value of the first 19 years + Present Value of the perpetuity = $63,931.44 + $100,000 = $163,931.44

User Nebffa
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