1. A perpetuity will pay X every year. The effective annual interest rate is 7.5%. The present value of this perpetuity 4 years before the first payment is 125,000. Find X.
2. Suppose you deposit $20,000 at the end of each of the next 30 years into a retirement account. Immediately after your last deposit, you take the entire accumulated value in your account and purchase a 20-year annuity, which will pay you X at the beginning of each year for 20 years. The price of this 20-year annuity is equal to the present value (at the time you purchase the annuity) of the 20 annual cash flows. The effective annual interest rate throughout the entire 50-year period is 10%. Find X.