Exam 4: Time Value of Money

Midway through the life of an amortized loan, the percentage of the payment that represents interest could be equal to, less than, or greater than to the percentage that represents repayment of principal. The proportions depend on the original life of the loan and the interest rate.

Suppose the U.S. Treasury offers to sell you a bond for $747.25. No payments will be made until the bond matures 5 years from now, at which time it will be redeemed for $1,000. What interest rate would you earn if you bought this bond at the offer price?

The present value of a future sum decreases as either the discount rate or the number of periods per year increases, other things held constant.

Time lines cannot be constructed in situations where some of the cash flows occur annually but others occur quarterly.

All other things held constant, the present value of a given annual annuity increases as the number of periods per year increases.

Disregarding risk, if money has time value, it is impossible for the future value of a given sum to exceed its present value.

How much would $1, growing at 3.5% per year, be worth after 75 years?

You plan to invest in securities that pay 8.0%, compounded annually. If you invest $5,000 today, how many years will it take for your investment to grow to $9,140.20?

Last year Tempe Corporation's sales were $525 million. If sales grow at 7.5% per year, how large (in millions) will they be 8 years later?

Your sister turned 35 today, and she is planning to save $7,000 per year for retirement, with the first deposit to be made one year from today. She will invest in a mutual fund that's expected to provide a return of 7.5% per year. She plans to retire 30 years from today, when she turns 65, and she expects to live for 25 years after retirement, to age 90. Under these assumptions, how much can she spend each year after she retires? Her first withdrawal will be made at the end of her first retirement year.

Suppose an ExxonMobil Corporation bond will pay $4,500 ten years from now. If the going interest rate on safe 10-year bonds is 4.25%, how much is the bond worth today?

Your company has just taken out a 1-year installment loan for $72,500 at a nominal rate of 11.0% but with equal end-of-month payments. What percentage of the 2nd monthly payment will go toward the repayment of principal?

If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by multiplying the periodic rate by the number of periods per year.

What's the future value of $1,500 after 5 years if the appropriate interest rate is 6%, compounded semiannually?

Disregarding risk, if money has time value, it is impossible for the present value of a given sum to exceed its future value.

What is the PV of an ordinary annuity with 10 payments of $2,700 if the appropriate interest rate is 5.5%?

Your father paid $10,000 (CF at t = 0) for an investment that promises to pay $750 at the end of each of the next 5 years, then an additional lump sum payment of $10,000 at the end of the 5th year. What is the expected rate of return on this investment?

If we are given a periodic interest rate, say a monthly rate, we can find the nominal annual rate by dividing the periodic rate by the number of periods per year.

You deposit $1,000 today in a savings account that pays 3.5% interest, compounded annually. How much will your account be worth at the end of 25 years?

You deposit $500 today in a savings account that pays 3.5% interest, compounded annually. How much will your account be worth at the end of 25 years?