FINC 331 WEEK 3 HOMEWORK HINTS

FINC 331 WEEK 3 HOMEWORK HINTS

Overview This week the homework significantly more difficult. Yikes! Every question requires the understanding of the formula. That said most of the questions are straight forward. So – don’t worry – I am confident that if you follow my steps in the following slides, you will be successful. These questions deal with: 1. 2. 3. 4. 5. Single Period Investments Simple interest Compound interest Present value of a single amount, and of annuities Future value of a single amount, and of annuities

Single Period Investments A single period investment is one where the time frame is just one period. The period is usually one year, but it could be 1 day, one month, etc. If the time period is anything other than a year, the problem will tell you. I will come back to this in a later slide. The formula for a single period investment is FV PV(1 i) Where FV the future value one period from now PV the value of the investment today i the annual interest rate Example: What is the future value in one year of 100 invested at 5%? FV 100 x (1 .05) 105 NOTE – remember to convert the percentage interest rate to a decimal!

Simple Interest Simple interest means that just the principal earns interest. For example, in our previous slide the investment earned 5 per year. After 2 years, this same investment would be worth 110 After 3 years, it is worth 115 and so on. Only the principal amount of 100 is earning interest each year. The formula is: Simple interest: FV PV (1 rt) Where rt equals the interest rate multiplied by the time period. 110 100 x (1 (5x2)) 115 100 x (1 (5x3))

Compound Interest Compound interest means that both the principal and the interest earn interest. In our previous example only the 100 earned interest. With compound interest, the 5 will earn interest too. Where FV the future value “t” periods from now PV the value of the investment today i the annual interest rate t the number of periods Example: What is the future value in 3 years of 100 invested at 5%? FV 100 x (1 .05)3 115.76 So, if the interest also earns interest, then the investment grows faster.

Future value Future value takes the idea of compounding and allows us to compute the value at some point in the future of a sum that we have today, or of a stream of payments that we expect to receive. A stream of cash flows that are the same amount is called an annuity. Because the formula can get very unwieldy if there are a lot of payments or period, we can use a special table that allows us to simplify the formula. You can also use a financial calculator. We will use the tables because they are accessible for everyone.

Interest rates Periods

Example To use the table all you have to do is go across to the interest rate, and down to the number of periods. Multiply the resulting number by the invested amount. For example, if we invest 1000 for 5 years at 1.5% we would have: 1000 x 1.07728 1,077.28

Annuities If we have a stream of payments, we can use the Future value of an annuity table to figure it out. Example: 200 payment made monthly for 2 years. The interest rate is 12%. Be careful! This is tricky. There are actually 24 periods!!! (2 years x 12 months) And the interest rate is stated as an annual rate, so each payment only is at 1%. (12% / 12 months) FV 200 x 26.97346 5,394.69 NOTE – see the table on the next slide. We go over to the 1% column, and then down to the 24 row.

Future Value of Ordinary Annuity

Present Value Present value tells us what some amount that will be received in the future is worth today. To compute Present value, we also can use the tables just like we did for Future value. There is one for a single amount, and for a stream of cash flows (annuity). See the tables in the next two slides.

Present Value of 1

Present Value of Ordinary Annuity

Resources for specific questions Question #7 (the problem is titled #5-12 in case the homework program scrambles the questions) You will need an annuity calculator to get the correct answer. The reason for this is that the number of periods is so large that most tables do not have it listed. I could not find one, and I looked at a lot of them! So, just plug your numbers into this calculator. NOTE that the growth rate is 0. http://www.calculatorsoup.com/calculators/financial/future-value-annuity-calculator.php

Question #8 This question asks for the PV of an annuity after only 4 of the 5 years. Therefore, the number of periods is computed on the 4 years worth of payments. (4 x 12) I had to create an annuity table for you, so use this one on the next slide.