12. Derek can deposit $272.00 per month for the next 10 years into an account at Bank A. The first deposit will be made next month. Bank A pays 12.00% and compounds interest monthly. Derek can deposit $2,570.00 per year for the next 10 years into an account at Bank B. The first deposit will be made next year. Bank B compounds interest annually. What rate must Bank B pay for Derek to have the same amount in both accounts after 10 years?

21. What is the value today of a money machine that will pay $2,021.00 per year for 27.00 years? Assume the first payment is made 8.00 years from today and the interest rate is 8.00%.

9. Derek plans to retire on his 65th birthday. However, he plans to work part-time until he turns 71.00. During these years of part-time work, he will neither make deposits to nor take withdrawals from his retirement account. Exactly one year after the day he turns 71.0 when he fully retires, he will begin to make annual withdrawals of $157,756.00 from his retirement account until he turns 88.00. After this final withdrawal, he wants $1.94 million remaining in his account. He he will make contributions to his retirement account from his 26th birthday to his 65th birthday. To reach his goal, what must the contributions be? Assume a 7.00% interest rate.