Present value (11) What would the present value be if this was a perpetuity? Annuity payment Interest rate Present value A 20-year-old student wants to save $5 a day for her retirement. Every day she places $5 in a drawer. At the end of each year, she invests the accumulated savings ($1,825) in a brokerage account with an expected annual return of 8%. (12) If she keeps saving in this manner, how much will she have accumulated at age 65? Savings per year Interest rate Years until retirement Money at retirement (13) If a 40-year-old investor began saving in this manner, how much would he have at age 65? Savings per year Interest rate Years until retirement Money at retirement (14) How much would the 40-year-old investor have to save each year to accumulate the same amount at 65 as the 20-year-old investor? Interest rate Required annual savings (15) What is the present value of the following uneven cash flow stream? The annual interest rate is 4%. 0 1 2 3 4 | | | | | $100 $300 $300 -$50 Interest rate Present value (16) What is the EAR corresponding to a nominal rate of 4% compounded semiannually? Compounded quarterly? Compounded daily? Nominal rate Effective rate (semiannually) Effective rate (quarterly) Effective rate (daily) (17) What is the future value of $100 after 3 years under 4% semiannual compounding? Quarterly compounding? Years Present value Future value (semiannually) Future value (quarterly) (18) Construct an amortization schedule for a $1,000, 4% annual interest loan with 3 equal installments. (19) What is the annual interest expense for the borrower and the annual interest income for the lender during Year 2? N I/YR PV FV PMT The following is an amortization table of this $1,000 loan. Year Loan amount Payment Paid toward Interest Paid toward Principal Balance 1 2 3