1.What is the present value of a security that will pay $27,000 in 20 years if securities of equal risk pay 3% annually? Do not round intermediate calculations. Round your answer to the nearest cent.

2. Your parents will retire in 23 years. They currently have $200,000 saved, and they think they will need $800,000 at retirement. What annual interest rate must they earn to reach their goal, assuming they don't save any additional funds? Round your answer to two decimal places.

3. If you deposit money today in an account that pays 6% annual interest, how long will it take to double your money? Round your answer to two decimal places.

4. What's the future value of a 10%, 5-year ordinary annuity that pays $600 each year? If this was an annuity due, what would its future value be? Do not round intermediate calculations. Round your answers to the nearest cent.

5. You want to buy a car, and a local bank will lend you $20,000. The loan will be fully amortized over 5 years (60 months), and the nominal interest rate will be 5% with interest paid monthly. What will be the monthly loan payment? What will be the loan's EAR? Do not round intermediate calculations. Round your answer for the monthly loan payment to the nearest cent and for EAR to two decimal places.

6. Complete an amortization schedule for a $40,000 loan to be repaid in equal installments at the end of each of the next three years. The interest rate is 9% compounded annually. If an amount is zero, enter "0". Do not round intermediate calculations. Round your answers to the nearest cent.

7. An investment will pay $50 at the end of each of the next 3 years, $250 at the end of Year 4, $300 at the end of Year 5, and $500 at the end of Year 6. If other investments of equal risk earn 10% annually, what is its present value? Its future value? Do not round intermediate calculations. Round your answers to the nearest cent.

8. Find the present value of $800 due in the future under each of these conditions:

1. 6% nominal rate, semiannual compounding, discounted back 9 years. Do not round intermediate calculations. Round your answer to the nearest cent. $

2. 6% nominal rate, quarterly compounding, discounted back 9 years. Do not round intermediate calculations. Round your answer to the nearest cent. $

3. 6% nominal rate, monthly compounding, discounted back 1 year. Do not round intermediate calculations. Round your answer to the nearest cent. $

4. Why do the differences in the PVs occur?