1. The Time Value of Money Lesson 16.1

2. Starter

3. Objectives Students will be able to –Use a formula to find the future value of a series of payments –Use the TVM Solver on the calculator to Find the future value of a series of payments Find the present value of a future series of payments

4. Now let’s do a geometric series:

5. First Investment Question If you invest $100 at 10% annual interest, how much will it be worth in 40 years? Simple interest: –I = Prt = $100 x.1 x 40 = $400 –Add the original $100 investment to get $500 Compound interest: –After one year you have $100(1.1) –After two years you have $100(1.1)(1.1) –After 40 years you have $100(1.1) 40 = $4525.93

6. Second Investment Question If you invest $100 at 10% annual interest every year for 40 years, how much will you have at the end of 40 years? The first investment will be worth $100(1.1) 40 = $4525.93 The next investment will be worth $100(1.1) 39 = $4114.48 Do this for 38 more investments and add them all up to get the answer. OR:

7. Use a formula

8. Now let’s make it realistic If you invest $100 at 10% annual interest every month, how much will it be worth in 40 years? Notice this is the same question, but with two important modifications: –There are 480 months in 40 years, so use n=480 –The 10% annual interest rate must be divided by 12 to get a monthly rate 0.1 / 12 = 0.008333… so use r = 1.0083333…

9. Answer:

10. Find the Finance Screen on your TI-83 and go to the TVM Solver Here are the meaning of each line: –N is the number of years or months involved –I% is the ANNUAL interest rate –PV is the present value of the account For savings, start with zero For loan payoff, start with the loan amount –PMT is the annual or monthly payment Enter the amount as a NEGATIVE number –FV is the future value of the account –P/Y (payments per year) and C/Y (number of compoundings per year) should agree For monthly savings or payments use 12 For annual savings or payments use 1 –PMT: END/BEGIN Choose BEGIN for savings Choose END for loan payments

11. Set up the calculator to answer the last question N = 480 I% = 10 PV = 0 PMT = -100 FV Skip this for now P/Y = 12(Note that C/Y changed to 12) PMT: BEGIN Go back to FV and tap ALPHA : SOLVE –FV tells you the future value –Note it is the same as we calculated by formula

12. Practice with the TVM Solver How much would $200 per month at 10% grow to in 40 years? Change the interest to 12%. FV? How much per month is needed at 12% to grow to $5,000,000 in 40 years? If you borrow $20,000 to buy a car at 6% for 5 years how much will be the monthly payment? Borrow $400,000 at 5.5% for 30 years to buy a $500,000 starter house. How much are your monthly payments?

13. California Lottery Payments If you win $1,000,000 in the lottery, they pay $50,000 per year for 20 years. Use the calculator to find the present value of this series of payments assuming 5% annual interest. –Note that FV is 0: That’s what they owe you when the payments are done –Note also that there is 1 payment per year, not 12 You should get an answer of $654,266.04 –This is the amount they will offer you if you want a lump sum payment –Try it at different interest rates and see what you get

14. Objectives Students will be able to –Use a formula to find the future value of a series of payments –Use the TVM Solver on the calculator to Find the future value of a series of payments Find the present value of a future series of payments