Compound Interest Howard Godfrey, Ph.D., CPA Copyright © 2011, Dr. Howard Godfrey Edited August 3, 2011

Review of compound interest concepts and procedures. 1.Future value of an investment made today. 2.Present value (today) of an amount in the future. 3.Future value of an annuity (series of payments). 4.Present value of an annuity (series of payments).

Future value of an investment made today. I will invest $1,000 today (Jan. 1, Year 1) in a savings account. My savings account will earn interest at the rate of 10% per year, compounded annually. How much money will be in the account in 3 years? (Dec. 31, Year 3)?

Conclusion. If you invest $1,000 today in a savings account earning 10% interest per year, your account will have a balance of $1,331 in three years.

Present value of a payment to be made in the future. I bought computer today. Price is $1,000, payable in 3 years. I do not pay interest on this debt. Assume I normally pay 10% when borrowing money. What is present value of the $1,000 to be paid in 3 years?

Conclusion. The seller of the computer should be willing to accept $ in full payment of the computer today, if the seller uses the same interest rate. If the seller invests $ today in a savings account earning 10% interest, the balance in 3 years will be $1,000.

Future value of an annuity (periodic payments) I will save $1,000 each year and deposit that amount in a savings account on the last day of each of the next 3 years. My savings account will earn 10% per year. How much money will be in my account at the end of 3 years?

Conclusion If I invest $1,000 in a savings account at the end of each year (total deposits of $3,000) the account balance will be $3,310 in three years. [Note this also applies for other business transactions involving periodic payments.]

Present value of an annuity (series of payments). I bought computer today. My price is $3,000, payable in $1,000 at the end of year 1, $1,000 at the end of year 2 and $1,000 at the end of year 3. I do not pay interest on this debt. Assume I normally pay 10% on borrowed money. What is present value of the payments?

Conclusion The actual purchase price of the computer is $2,486.85, if a discount rate of 10% is used (with annual compounding). A little over $500 is for interest for deferred payment. We use these approaches when computing present values (PV) of lease payments, PV of bonds, PV of potential capital budgeting investments, etc.

NTD Company issues bonds. [1 of 3] NTD Company issues bonds with a face value of $100,000 on Jan. 1, These bonds pay interest twice per year at the annual rate of 9%. Interest is paid on 6-30 and Bonds mature in 2 years [ ]. Bonds were sold at a price to yield 10% per year. Please compute the price of the bonds and complete the amortization table on the next slide.

Market rate if price exceeds par value. What is the market rate of interest for a bond issue which sells for more than its par value? a. Less than rate stated on the bond. b. Equal to rate stated on the bonds c. Higher than rate stated on the bond. d. Rate is independent of rate stated on the bonds. (Source: CPA)

Market rate if price exceeds par value. What is the market rate of interest for a bond issue which sells for more than its par value? a. Less than rate stated on the bond. Reason. Bond has rate of interest that is better than the market demands. Market pays extra for this bond. Amount paid for the bond is based on present value of cash flows.

NPV Example Original investment (cash outflow): $6,075 Useful life: four years Annual income generated from investment (cash inflow): $2,000 Minimum desired rate of return: 10%

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