4. What is an annuity? How does an ordinary annuity differ from an annaity due? Where do we run into annuities - give two examples. 5. Find the future value of an ordinary annuity of $100 per year for three years at 10% rate of retum. Calculate future value using a simple equation and then using a financial calculator. 6. What if the above annuity is an annuity due? How would your calculation and answer change? 7. Suppose Jane has agreed to make \$457 payments at the end of every year for 7 years on a loan. How much would she have to pay today, if she decided to pay off the loan in one lump sum? The interest rate on the loan is 10%. 8. What if Jane is to make the loan payments at the beginning of every year, starting today. How much does she have to pay today to pay off the loan in one lump sum? The interest rate is still 10%. 9. Suppose you purchase a home for $250,000. You have a down payment of $50,000 and plan to borrow the rest. You can lock in a 30-year fixed rate mortgage of 5.84% today. Calculate the amount of your monthly payments. 10. Suppose a business plans to make annual payments on a $650,000 loan. The term of the loan is 5 years. The interest rate on the loan is 6%. Amortize the loan by hand and using your financial calculator. Show the calculations of yearly payment, interest, principal repayment, and remaining principal balance in the space below. 11. What is a perpetuity? How is the value today of the perpetuity calculated? Assume annual payments of $300 forever. The market rate of interest on similar risk cash flows is 10%. 12. Use an annuity example to explain why a perpetuity can be valued