A dollar in hand today is worth more than a dollar promised at some future time. Money is related to time. 1 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

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Bank Cash Compound Interest Compounding Decision Interest Interest Rate Investing Investment Money Opportunity Cost Principal Reinvesting Savings Savings Account Simple Interest Trade-Off 3 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

Principal (P) the original amount invested to which interest is applied 4 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

Interest Rate (R) the percentage that is used to calculate interest expressed as a fraction or decimal 5 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

Time Factor (T) the length of time for which interest will be charged 6 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

Simple Interest Simple Interest – interest on an investment if not reinvested, so interest is earned each period on the original investment (principal) only 7 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

Investing for a Single Period – SIMPLE INTEREST Formula I (interest) = P (principal) x R (rate) x T (time) Problem: I = __?___ P-$100 R-10% T-1 year) 8 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

Investing for a Single Period $100 deposit into a savings account 10% interest rate per year annually) ?? How much will you have in one year? 9 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

Investing for a Single Period – SIMPLE INTEREST (formula) I (interest) = P (principal) x R (rate) x T (time) In our situation: (I = $10) = (P-$100) x (R-10%) x (T-1 year) 10 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

Investing for a Single Period – SIMPLE INTEREST I (interest) = P (principal) x R (rate) x T (time) In our situation: (I = $10) = (P-$100) x (R-10%) x (T-1 year) Your investment has grown to $110 ! (P = $100) + (I = $10) = $ “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

Reinvesting Leaving principal and adding the interest to accumulate interest 12 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

Compounding...the process of leaving an initial investment plus accumulated interest in a bank for more than one period 13 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

What if you leave that money in the bank? What would you have after two (2) years, if the interest rate remains the same? I (interest) = P (principal) x R (rate) x T (time) (_______?) = P($110) x R (10%) x T (1 year) 14 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

What if you leave that money in the bank? I (interest) = P (principal) x R (rate) x T (time) (I = _______?) = P($110) x R (10%) x T (1 year) 11 = $110 x 10% x 1 yr Your investment has grown to $121 ! (P = $110) + (I = $11) = $ “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

Compound Interest Earning interest on interest through reinvesting. The result of compounding. 16 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

What if you leave that money in the bank? Your investment has grown to $121! (P = $110) + (I = $11) = $121 This $121 has four (4) parts: 1) $100 original principal 2) $10 interest earned the first year 3) $10 interest earned on principal the second year 4) $1 interest earned the second year on interest paid in the first year (I first year = $10) x (R = 10%) = I second year $1 17 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

Future Value …cash value of an investment at a particular time in the future. 18 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

Future Value What is the future value of the $100 principal at the end of two (2) years? What was the amount of money to which the $100 investment would grow over two years at an interest rate of 10%? 19 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

Investing for a Single Period – SIMPLE INTEREST Formula I (interest) = P (principal) x R (rate) x T (time) Problem: I = __?___ P-$100 R-10% T-1 year) 20 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

What if you leave that money in the bank? I (interest) = P (principal) x R (rate) x T (time) (I = _______?) = P($110) x R (10%) x T (1 year) 11 = $110 x 10% x 1 yr Your investment has grown to $121 ! (P = $110) + (I = $11) = $ “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

Opportunity Cost The second-best alternative (or the value of that alternative) that must be given up when scarce resources are used for one purpose instead of another. The cost of any decision includes the cost of the best forgone opportunity. 22 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

Opportunity Cost What are some things you can do or buy with $10? 1. _______________________________ 2. _______________________________ 3. _______________________________ 4. _______________________________ 23 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

Trade-Off The giving up of one benefit or advantage in order to gain another regarded as more favorable. The trade-off between money now and money later depends on, among other things, the rate of interest you can earn by investing. The trade-off in our $100 investment grown to $121 is in all the things that were ‘given up’ in order to reinvest the original principal and the interest earned. 24 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

Opportunity Cost The cost of any decision includes the cost of the best forgone opportunity 25 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

What Would YOU Do? Suppose someone owed you $300. Would you rather have this money paid back now, in one payment, or later in installment payments? Does it make any difference? 26 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved

Investing for a Single Period – SIMPLE INTEREST (formula) I (interest) = P= $300 (principal) x R (rate) x T (time) 27 “Time Value of Money” MONEY MATTERS Copyright © Texas Education Agency, All rights reserved