## Section 3 Review

- Pages:
- 9
- School:
- University of Texas at Austin
- Course:
- Fin 320f - Foundations of Finance

**Unformatted text preview: **

FIN 320F Foundations of Finance Section 3 Review The Time Value of Money 1) The value of money changes over time. a) Money in hand must be compounded to determine its value in the future. Compounding is the process of adding interest to the beginning balance and previously accrued interest. In other words, compounding allows us to earn (or pay) interest on interest. i) The larger the compound interest rate, the larger the future value. $100 in a savings account that pays 5% will be worth more in the future than $100 in a savings account that pays 2%. ii) The more frequent the compounding, the greater the future value. $100 at 12% compounded monthly will have a higher future value than $100 at 12% compounded annually. b) Money that will be received at some moment in the future must be discounted to determine its value today. In other words, a dollar received tomorrow is worth less than a dollar received today. Discounting is the opposite of compounding. i) The larger the discount rate, the smaller the present value. A $100 sweater on sale at Target for a 10% discount has a present value of $90. The same sweater on sale for a 20% discount has a present value of only $80. ii) The more frequently the discount rate is applied, the smaller the present value. This is simply compounding in reverse. 2) Lump sums are one-off chunks of cash, for instance, the down-payment on a house or car, a one-time gift or bonus, or the repayment of principal on a bond. a) To calculate the present and future values of lump sums, or to determine the periodic rate or the number of periods, we need the following data: i) m the number of payments or compounding or discounting periods per year ii) r the annual rate of return or interest rate Note: the periodic rate = r ÷ m = Big I% in a financial calculator iii) n the total number of years Note: the total number of periods or payments = n m = Big N in a financial calculator iv) PV Present Value, the value of the lump sum at time zero mn m r1 1FV PV v) FV Future Value, the value of the lump sum at the end of n × m periods mn m r1PV FV 3) Annuities are streams of equal payments that are equally spaced in time, eg. mortgage loan payments due on the first of each month, or bond coupon payments paid every six months. a) There are various types of annuities: i) An ordinary annuity has its first payment at the end of the period. This is by far the most common type of annuity. All loans (student loans, car loans, mortgage loans, etc.) SourceDocument.docx Page 1 of 11 FIN 320F Foundations of Finance Section 3 Review are ordinary annuities. For example, you ...

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