3.5 interest problems
- 2. Simple Interest • Simple Interest means interest is only paid/charged to your account once per year. A P (1 r) t • A = the balance (or ending amount) after interest is added • P = the principle (or beginning amount) • r = the interest rate earned/charged per year, written as a decimal • t = the term or time (the number of years)
- 3. Writing Functions • Write a function definition for each situation: • Principle = $158, interest rate = 3.9% • Sara opens an account with $3210 and earns 8% annually.
- 4. You Try! • Write a function definition for each: • Principle = $1250, interest rate = 12% • Joe earns 2 ½ % on an initial amount of $79.30.
- 5. Identifying Variables • Identify any of the variables A, P, r, t in the following situations: • A = 1468(1 + 0.05)t • 3800 = P(1.0425)5
- 6. You Try! • Identify A, P, r, t : • A = 250(1 + 0.03)t • 2100 = P(1.123)10
- 7. Solving Simple Interest Problems 1. List parameters: A, P, r, t 2. Write function 3. Identify what to solve for, then solve Example 1: • George took out a loan for $7200, and the bank is charging simple interest at a rate of 3.25%. How much will he owe at the end of three years?
- 8. Example 2 • After 8 years, Fred owes $10000 on a loan for which he is charged 12.5% interest. What was his original debt?
- 9. You Try! • Tom has $1500 in his account after earning 3% interest for 7 years. How much did he originally invest?
- 10. Compound Interest • Compound Interest means interest is added multiple times per year. A P 1 r n nt • A = the balance (or ending amount) • P = the principle (or beginning amount) • r = the interest rate, written as a decimal • n = number of times per year interest is compounded • t = the term (# of years)
- 11. Compounding Vocab • Annually • Semi-annually • Quarterly • Monthly • Weekly • Daily n=1 n=2 n=4 n = 12 n = 52 n = 365
- 12. Example 1 • You deposit $300 in an account that pays 5% annual interest. Find the balance after 12 years if the interest is compounded: • Quarterly? A= • Monthly? • You Try! • Weekly? P= r= n= t=
- 13. Example 2 • Write a function definition for this situation: • Taylor wants to have $10,000 after five years with a bank account earning 6.8% interest compounded semi-annually. •A= •P= •r= •n= •t=
- 14. You Try! • Write a function definition for this situation: • Desmond invests $8,000 for 4 years in a bank account earning 5 ¼ % interest compounded monthly. •A= •P= •r= •n= •t=
- 15. Example 3 • You want to have $23,000 after 4 years to buy a car. • Find the amount you should deposit now if the account pays 5.9% annual interest compounded quarterly. •A= •P= •r= •n= •t=
- 16. You Try! • New parents want to have $50,000 after 18 years for their child’s college. • Find the amount they should deposit now if the account pays 6.8% annual interest compounded monthly. •A= •P= •r= •n= •t=