Financial Math

(2pts) A and B spend the same amount of money to purchase different annuities. A buys a perpetuity-immediate, which makes annual payments of 50. B buys a 10-year annuity- immediate with annual payments, where the first payment is 45 and each subsequent payment is k% larger than the previous year's payment. Both annuities use an annual effective interest rate of k%. Find k. (Answer: 12.5.) 6. 7. (3pts) Two annuities have equal present values. The first is an annuity-immediate with quarterly payments of SX for 10 years. The second is an increasing annuity-immediate with 10 annual payments, where the first payment is $500 and subsequent payments increase by $50 per year. Find X if the annual effective interest rate is 5%. (Answer: 173.03.) 8. (3pts) A purchases a 10-year annuity-immediate with annual payment of 10X. B purchases a 10-year decreasing annuity-immediate, where the annual payment at the end of year 1 is 50 and each subsequent payment is reduced over what was paid in the previous year by the amount X. Both annuities have the same present value if the annual effective interest rate is 7%. Find X, where X