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44 45 d. Finding the rate of return provided by the security 46 Cost of security (PV) $1,000 47 Future value of security (FV) $3,000 48 Number of years (N) 6 #N/A 49 Rate of retum (1) 50 51 e. Calculating the number of years required to double the population 52 Current population in millions (PV) 35.9 53 Growth rate (1) 4% 54 Doubled population in millions (FV) 55 Number of years required to double (N) 56 57 f. Finding the PV and FV of an ordinary annuity 58 Annuity (PMT) 59 Interest rate (1) 60 Number of years (N) 61 Present value of ordinary annuity (PV) #N/A 62 Future value of ordinary annuity (FV) #N/A 63 64 g. Recalculating the PV and FV for part f if the annuity is an annuity due 65 Present value of annuity due (PV) 66 Future value of annuity due (FV) #N/A #N/A 67 68 h. Recalculating the PV and the FV for parts a and c if the interest rate is semiannually compounded 69 Future value (FV) 70 Present value (PV) #N/A #N/A 71 72 1. Finding the annual payments for an ordinary annuity and an annuity due 73 Present value (PV) $1,000 74 Discount rate (1) 6% 75 Number of years (N) 12 76 Annual payment for ordinary annuity (PMT,) 77 Annual payment for annuity due (PMT₂) #N/A #N/A 78 79 Finding the PV and the FV of an investment that makes the following end-of-year payments 80 Year Payment 81 1 $100 82 2 $200 83 3 $500 84 85 Interest rate (1) 6% 86 Present value of investment (PV) 87 Future value of investment (FV) 88 ∞∞∞ ∞ ∞0 00 00 HIVA $1,000 11% 6 #N/A #NA #N/A #N/A
k. Five banks offer nominal rates of 4% on deposits, but A pays interest annually, B pays semiannually, C pays quarterly, D pays monthly, and E pays daily. Assume 365 days in a year. 1. What effective annual rate does each bank pay? If you deposit $4,000 in each bank today, how much will you have in each bank at the end of 1 year? 2 years? Round your answers to two decimal places. B C D EAR % % % % FV after 1 year $ $ $ $ FV after 2 years $ $ $ $ $ 2. If the TVM is the only consideration, what nominal rate will cause all of the banks to provide the same effective annual rate as Bank A? Round your answers to two decimal places. B Nominal rate % 3. Suppose you don't have the $4,000 but need it at the end of 1 year. You plan to make a series of deposits- annually for A, semiannually for B, quarterly ford monthly for D, and daily for E-with payments beginning today. How large must the payments be to each bank? Round your answers to the nearest cent. A C D Payment $ 4. Even if the five banks provided the same effective annual rate, would a rational Investor be indifferent between the banks? It is more likely that an investor would prefer the bank that compounded frequently. L Suppose you borrow $16,000. The interest rate is 6%, and it requires 4 equal end-of-year payments. Set up an amortization schedule that shows the annual payments, interest payments, principal repayments, and beginning and ending loan balances. Round your answers to the nearest cent. If your answer is zero, enter "0",
h. What will the FV and the PV for parts a and c be if the interest rate is 8% with semiannual compounding rather than 8% with annual compounding? Round your answers to the nearest cent. FV with semiannual compounding: $ PV with semiannual compounding: $