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