1. Compound Interest Problems

2. Lesson Objectives Use the compound interest formula to solve problems Use the compound interest formula to solve problems Simple interest I = P*r*t Simple interest I = P*r*t Compound interest Compound interest Continuously compounded interest Continuously compounded interest A = Pe rt

3. Vocabulary simple interest principal rate of interest compound interest

4. The formulas… n = # times compounded / year r = rate t = time (in years) P= principal(initial \) amt. Continuously compounded interestA = Pe rt Simple interest I= (P*r*t) Compound interest

5. The table shows some common compounding periods and how many times per year interest is paid for them. Compounding PeriodsTimes per year (n) Annually1 Semi-annually2 Quarterly4 Monthly12

6. Example 1-2 Suppose $10,000 is invested at 5.4%, compounded monthly. a) What is the balance after 2 yrs? 5 yrs?

7. David invested $1800 in a savings account that pays 4.5% interest compounded semi- annually. Find the value of the investment in 12 years. Example 3: You Try! Use the compound interest formula. Substitute. = 1800(1 + 0.0225) 24 Simplify. A = P(1 + ) rnrn nt = 1800(1 + ) 0.045 t 2 2(12) = 1800(1.0225) 24 Add inside the parentheses.

8. #3 Continued After 12 years, the investment will be worth about $3,070.38. ≈ 1800(1.70576) Find (1.0225) 24 and round. ≈ 3,070.38 Multiply and round to the nearest cent.

9. Example 4-5 Suppose $5,000 is invested at 6%, compounded continuously. a) What is the balance after 2 yrs? You try: 5 yrs?

10. Example 6 I have $2,500 to invest and need $4,000 in 6 years. I found an account that pays 8% interest (compounded daily) A) At this rate, will I get my money?

11. Kia invested $3700 in a savings account that pays 2.5% interest compounded quarterly. Find the value of the investment in 10 years. Guided Practice. Example 7 – YOU TRY! Use the compound interest formula. Substitute. = 3700(1 + 0.00625) 40 Simplify. A = P(1 + ) rnrn nt = 3700(1 + ) 0.025 t 4 4(10) = 3700(1.00625) 40 Add inside the parentheses.

12. Check It Out! Example 7 Continued After 10 years, the investment will be worth about $4,747.20. ≈ 3700(1.28303) Find (1.00625) 40 and round. ≈ 4,747.20 Multiply and round to the nearest cent.

13. 4 CORNERS : Part I Theresa invested $800 in a savings account that pays 4% interest compounded quarterly. Find the value of the investment after 6 years. A.$1156. 79 B.$1015.79 C.$1014.39 D.$1015.85

14. STOP! Hw

15. Ex.8 Suppose $10,000 is invested at 5.4%, compounded monthly. Using Log/Ln to find “t”. b) What is the doubling time?

16. Ex.9 Suppose $5,000 is invested at 6%, compounded continuously. b) What is the doubling time?

17. Ex.10 I have $2,500 to invest and need $4,000 in 6 years. I found an account that pays 8% interest (compounded daily) B) What is the minimum rate I need to guarantee reaching this value?

18. Example 11 I want to retire with $1,000,000 in thirty years. I can get a rate of 7%. How much will I need to invest now if it is compounded monthly?

19. Example 11 (cont’d) You Try…What about if “Continuously”?