Who is very Interested in Compounding Mr. Peter Richard Who is very Interested in Compounding Your problems hopes that you are interested in this very Compounded Lesson!

Compound interest is interest paid not only on the principal, but also on the interest that has already been earned. The formula for compound interest is below. A = P(1 + ) r n nt A is the final dollar value, P is the principal, r is the rate of interest, t is the number of years, and n is the number of compounding periods per year.

The table shows some common compounding periods and how many times per year interest is paid for them. Compounding Periods Times per year (n) Annually 1 Semi-annually 2 Quarterly 4 Monthly 12

Additional Example 5: Applying Compound Interest David invested $1800 in a savings account that pays 4.5% interest compounded semi-annually. Find the value of the investment in 12 years. A = P(1 + ) r n nt Use the compound interest formula. = 1800(1 + ) 0.045 t 2 2(12) Substitute. = 1800(1 + 0.0225)24 Simplify. = 1800(1.0225)24 Add inside the parentheses.

Additional Example 5 Continued ≈ 1800(1.70576) Find (1.0225)24 and round. ≈ 3,070.38 Multiply and round to the nearest cent. After 12 years, the investment will be worth about $3,070.38.

Use the compound interest formula. Check It Out! Example 5 Kia invested $3700 in a savings account that pays 2.5% interest compounded quarterly. Find the value of the investment in 10 years. A = P(1 + ) r n nt Use the compound interest formula. = 3700(1 + ) 0.025 t 4 4(10) Substitute. = 3700(1 + 0.00625)40 Simplify. = 3700(1.00625)40 Add inside the parentheses.

Check It Out! Example 5 Continued ≈ 3700(1.28303) Find (1.00625)40 and round. ≈ 4,747.20 Multiply and round to the nearest cent. After 10 years, the investment will be worth about $4,747.20.

Lesson Quiz: Part I 1. A bank is offering 2.5% simple interest on a savings account. If you deposit $5000, how much interest will you earn in one year? 2. Joshua borrowed $1000 from his friend and paid him back $1050 in six months. What simple annual interest did Joshua pay his friend? $125 10%

Lesson Quiz: Part II 3. The Hemmings borrowed $3000 for home improvements. They repaid the loan and $600 in simple interest four years later. What simple annual interest rate did they pay? 4. Theresa invested $800 in a savings account that pays 4% interest compounded quarterly. Find the value of the investment after 6 years. 5% $1015.79

Time to Compound Yourself! Quiz: Page 479 # 16, 18, 34, 57 Homework: # 17, 19, 33, 58