Friday, October 13 th Finance

1. Friday, October 13thFinance Time is Money

2. Basic Math Operations First To remember the conventional order of operations, you can think of PEMDAS (You might remember this as "Please excuse my dear Aunt Sally.") • Parentheses • Exponents • Multiplication and Division • Addition and Subtraction This means that you should do what is possible within parentheses first, then exponents, then multiplication and division (from left to right), and then addition and subtraction (from left to right). If parentheses are enclosed within other parentheses, work from the inside out. Here are two examples: • 3 + 5 x 7 = ?3 + 5 x 7 = 3 + 35 = 38 • (1 + 3) x (8 - 4) = ?(1 + 3) x (8 - 4) = 4 x 4 = 16

3. Bank Account Math • Let's go over the math of bank accounts: Suppose we put $200 in a bank account and leave it there for a year. The bank account pays 5% interest at the end of each full year. After one year, after the 5% interest is paid, how much will be in the account? • Correct $210. • That's the $200 we started with, plus 5% of $200, which is $10

4. We can formally express it like this: • At 5% interest, $200 in the bank today will grow to $210 in one year. • $200 ×(1.05) = $210 Present Value ×( 1 + Interest Rate ) 

5. Future Value Present Value times (1 + Interest Rate)= Future Value in One Year Multiplying $200 by 1.05 is mathematically equivalent to adding 5% to it.

6. Let's go to two years. If we leave all the money in the bank for two years, how much will we have at the end? $220.00 or $220.50

7. $220.00 is Not correct. Your original $200 will earn another $10 interest, but you'll also get interest on the first year's interest. • Getting interest on interest is called 'compounding.‘ $220.50 is Correct! After one year you have $210.00. After the second year, you get 5% of $210, which is $10.50, in interest. Your new total is $210 + $10.50 = $220.50.

8. We can also express it like this: $200 ×(1.05)²  = $220.50 OR $200 times (1.05 squared)= $220.50 So again.. Present Value times ( 1+Interest Rate ) squared= Future Value

9. Now, let's do three years. If we leave all the money in the bank for three years, we have how much?You tell me?Here is a hintTo calculate how much we'll have in three years, we multiply by 1.05 three times, once for the first year, once for the second year, and once for the third year. ..The answer is…

10. By now, you can probably imagine the general formula for any number of years: • To calculate how much we'll have in a years, we multiply by 1.05 a times, once for each year.

11. Compounding • If interest is paid and compounded more frequently than once a year, the formula gets more complicated, but the basic idea is the same.

12. Our formula, again, is Future Value = Present Value ×( 1 + Interest Rate )ª, (1 + Interest Rate ) to the a power where a is the number of years in the future.

13. Using that, we can construct this table, based on a present value of $200 and an annual interest rate of 5%: • What would the answer be for year 4, 5 and 6. Years in the Future (6) 243.10 255.26 268.02 How $200 grows at 5% interest per year, compounded annually. ($200×1.05ª)  ($200 times 1.05 to the a power)

14. Now, let's use the same reasoning, except in reverse, to answer this question: How much would you need today to have $200 in one year? Assume that your only possible investment is this 5% bank account.

15. Which is the correct answer?$200 or $200/1.05 = $190.48 $200 is not correct - You don't need $200 now.You only need the amount that will grow to $200 if you leave it in the bank and earn interest for a year. Correct! You want the amount that will grow to $200 in one year. You want X such that X × (1.05) = $200. Divide both sides of this by 1.05, to get: X = $200/1.05, which calculates to X = $190.48.

16. Let’s take a break • Then to Present Value and Future Value • Then Discounted Rates