2. Starting today, Alexis deposits 500 into an account at the beginning of each month for 15 years. In return, she will receive a payment of X at the end of each year forever. The first payment of X will occur 16 years from today. At an annual effective yield rate of 4%, calculate X. A) 4,893 B) 4,909 C) 16,150 D) 50,125 E) 605,000

5. An annuity with 36 monthly payments has a first payment of 600 one month from today. Starting with the second payment, the next 15 monthly payments increase so that each payment is 4% larger than the previous payment. Furthermore, starting with the 17th payment, the next 20 monthly payments decrease so that each payment is 5% smaller than the previous payment. What would be the accumulated value of this annuity immediately after the last payment, if the annual effective interest rate is 6%? A) 24,197 B) 26,312 C) 28,819 D) 28,892 E) 29,115

8. Tina and Angel both have 1500 a month to spend on housing and investing. Each of them takes out a mortgage of 200,000. Tina gets a 30-year mortgage with monthly payments at a rate of 6.5% convertible monthly. Angel gets a 20-year mortgage with monthly payments at a rate of 6.1% convertible monthly. Their first payment is due at the end of the month. Whatever leftover money from their 1500 a month, after paying their mortgage, goes to an investment in an annuity that earns an annual effective rate of 5%. How much is Tina behind Angel in her annuity at the end of 30 years? (Assume Angel still invests his money after his mortgage is paid off) A) 60,160 B) 61,785 C) 74,250 D) 75,970 E) Tina is ahead of Angel

13. Gavin deposits 1000 into an account that earns a nominal discount rate of 5% convertible semiannually for three years and a nominal discount rate of d convertible monthly for the next four years. If the account is worth 1600 in seven years, calculate d. A) 7.3% B) 7.5% C) 7.9% D) 8.1% E) 8.4%