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Future Values. I now have \(\$ 20,000\) in the bank earning interest of .5 percent per month. need \(\$ 30,000\) to make a down payment on a house. I can save an additional \(\$ 100\) per month. How long will it take me to accumulate the \(\$ 30,000 ?\)

Perpetuities. A local bank advertises the following deal: "Pay us \(\$ 100\) a year for 10 years and then we will pay you (or your beneficiaries) \(\$ 100\) a year forever." Is this a good deal if the interest rate available on other deposits is 8 percent?

Quoting Rates. Banks sometimes quote interest rates in the form of "add-on interest." In this case, if a 1 -year loan is quoted with a 20 percent interest rate and you borrow \(\$ 1,000\) then you pay back \(\$ 1,200 .\) But you make these payments in monthly installments of \(\$ 100\) each. What are the true APR and effective annual rate on this loan? Why should you have known that the true rates must be greater than 20 percent even before doing any calculations?

Effective Rates. First National Bank pays 6.2 percent interest compounded semiannually. Sccond National Bank pays 6 percent interest, compounded monthly. Which bank offers the higher effective annual rate?

Calculating Interest Rate. You borrow \(\$ 1,000\) from the bank and agree to repay the loan over the next year in 12 equal monthly payments of \(\$ 90 .\) However, the bank also charges you a loan-initiation fee of \(\$ 20,\) which is taken out of the initial proceeds of the loan. What is the effective annual interest rate on the loan taking account of the impact of the initiation fee?

Retirement Savings. You believe you will spend \(\$ 40,000\) a year for 20 years once you retire in 40 years. If the interest rate is 5 percent per year, how much must you save each year until retirement to meet your retirement goal?

Retirement Planning. A couple thinking about retirement decide to put aside \(\$ 3,000\) each year in a savings plan that carns 8 percent interest. In 5 years they will receive a gift of \(\$ 10,000\) that also can be invested. a. How much money will they have accumulated 30 years from now? b. If their goal is to retire with \(\$ 800,000\) of savings, how much extra do they need to save every year?

Real versus Nominal Rates. You will receive \(\$ 100\) from a savings bond in 3 years. The nominal interest rate is 8 percent. a. What is the present value of the proceeds from the bond? b. If the inflation rate over the next few years is expected to be 3 percent, what will the real value of the \(\$ 100\) payoff be in terms of today's dollars? c. What is the real interest rate? d. Show that the real payoff from the bond (from part b) discounted at the real interest rate (from part \(c\) ) gives the same present value for the bond as you found in part a.

Real versus Nominal Dollars. Your consulting firm will produce cash flows of \(\$ 100,000\) this year, and you expect cash flow to keep pace with any increase in the general level of prices. The interest rate currently is 8 percent, and you anticipate inflation of about 2 percent. a. What is the present value of your firm's cash flows for Years 1 through 5? b. How would your answer to (a) change if you anticipated no growth in cash flow?

Real versus Nominal Annuitics. a. You plan to retire in 30 years and want to accumulate enough by then to provide yourself with \(\$ 30,000\) a year for 15 years. If the interest rate is 10 percent, how much must you accumulate by the time you retirc? b. How much must you save each year until retirement in order to finance your retirement consumption? c. Now you remember that the annual inflation rate is 4 percent. If a loaf of bread costs \(\$ 1.00\) today, what will it cost by the time you retire? d. You really want to consume \(\$ 30,000\) a year in real dollars during retirement and wish to save an equal real amount each year until then. What is the real amount of savings that you need to accumulate by the time you retire? c. Calculate the required preretirement real annual savings necessary to meet your consumption goals. Compare to your answer to (b). Why is there a difference? f. What is the nominal value of the amount you need to save during the first year? (Assume the savings are put aside at the end of cach year.) The thirticth year?