1. Ira Schwab opens up a Schwab IRA and places $2,000 in his retirement account at the beginning of each year for 10 years. He believes the account will earn 5 percent interest per year, compounded quarterly. How much will he have in his retirement account in 10 years? Note, the mode of compounding and the mode of making your payments have to match in order to use the formula. Therefore, we must first find the effective rate of 5 percent compounded quarterly and then use that rate in the formula, with $2,000 as the annuity or payment made at the beginning of each period. The effective rate is (1+.05/4)4 - 1 = 0.0509. This rate is plugged into the formula for a future value of an annuity due as the i or rate per period:
2. The city of Glendale borrows $48 million by issuing municipal bonds to help build the Arizona Cardinals football stadium. It plans to set up a sinking fund that will repay the loan at the end of 10 years. Assume a 4 percent interest rate per year. What should the city place into the fund at the end of each year to have $48 million in the account to pay back their bondholders? This is a future value of an ordinary annuity problem. The formula is: