d. Finding the rate of return provided by the security Cost of security (PV) $1,000 Future value of security (FV) $3,000 6 Number of years (N) Rate of return (1) #N/A e. Calculating the number of years required to double the population 37.8 Current population in millions (PV) Growth rate (1) 3% Doubled population in millions (FV) #N/A Number of years required to double (N) #N/A f. Finding the PV and FV of an ordinary annuity Annuity (PMT) Interest rate (1) Number of years (N) Present value of ordinary annuity (PV) #N/A Future value of ordinary annuity (FV) #N/A g. Recalculating the PV and FV for part f if the annuity is an annuity due Present value of annuity due (PV) #N/A #N/A Future value of annuity due (FV) h. Recalculating the PV and the FV for parts a and c if the interest rate is semiannually compounded Future value (FV) #N/A #N/A Present value (PV) i. Finding the annual payments for an ordinary annuity and an annuity Present value (PV) $1,000 Discount rate (1) 10% Number of years (N) 12 Annual payment for ordinary annuity (PMT) #N/A Annual payment for annuity due (PMT) #N/A $1,000 16% 6 j. Finding the PV and the FV of an investment that makes the following end-of-year payments Year Payment 1 $100 2 $200 3 $400 Interest rate (1) 10% Present value of investment (PV) #N/A #N/A Future value of investment (FV) k. Five banks offer the same nominal rate on deposits, but A pays interest annually, B pays semiannually, C pays quarterly, D pays monthly, and E pays daily. (1) Calculating the effective annual rate for each bank and the future values of the deposit at the end of 1 year and 2 years Nominal rate (INOM) 9% Deposit (PV) $3,000 365 Number of days per year A B D E Formulas EAR A #N/A EAR FV after 1 year #N/A FV after 1 year FV after 2 years FV after 2 years #N/A (2) Calculating the nominal rates that will cause all of the banks to provide the same effective annual rate as Bank A B D E B Nominal rate (INOM) Nominal rate (INOM) #N/A (3) Calculating the amount of payment to be made annually for A, semiannually for B, quarterly for C, monthly for D, and daily for E Needed amount (FV) $3,000 Number of years (N) 1 A B D E A #N/A Payment (PMT) Payment (PMT) 1. Setting up the amortization schedule Original amount of mortgage (PV) Interest rate (1) Term to maturity, years (N) Formula #N/A Annual payment (PMT) Formulas $14,000 10% 4 Year 1 -234 Beginning Balance Payment Interest Repayment of Principal Ending Balance
