Chapter 3: Consumer Math Section 3.2: Simple & Compound Interest Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

Simple Interest SIMPLE INTEREST FORMULA I = PRT Simple interest is a percentage of a principal amount, calculated for a specific period, usually stated in years. I = Interest P = Principal. This is the base amount. R = Rate. The annual interest rate as a decimal. T = Time. Stated in years. SIMPLE INTEREST FORMULA I = PRT Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Simple Interest Example: Find the amount of simple interest for $2000 invested at an annual rate of 2.65% for 3 years. Also find the total amount returned at the end of the investment. I = PRT I = ($2000)(0.0265)(3) I = $159 The total amount, A, returned is the original principal, plus the interest. A = P + I A = $2000 + $159 A = $2159 Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

Compound Interest COMPOUND AMOUNT FORMULA Most loans and investments are not simple. If the interest is calculated at intervals and added to the principal more than once, we call it compounding. A = Total Amount. The Principal plus Interest. P = Principal. The original amount. r = Rate. Specifically, the annual rate as a decimal. n = Number of compoundings per year. t = Time, in years. COMPOUND AMOUNT FORMULA Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Compound Interest Pay attention to the critical difference between the formulas for simple interest and compound amounts. For simple interest, I = PRT yields ONLY the interest, which means, in order to find the total amount, A, returned at the end of the term, we add the interest to the original principal. A = P + I. For compound amounts, A = P(1 + r/n)nt gives us the total amount, A. So, in order to find the interest alone, we need to subtract the principal, P, from the amount, A. I = A – P. Also, be sure to recognize if the question is asking for interest, total amount, rates or time. Always be sure to answer the question that has been asked! Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Compound Interest When using your calculator to compute a compounded amount, make use of the parentheses keys and be sure to pay attention to the order of operations for the exponentiation. Example: Use your calculator to find the following. Type: 5000 1 0.085 12 12 5 A = $7636.50 × ( + ÷ ) xy ( × ) = Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates

Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates Compound Interest Example: Find the total amount and the interest earned for $5000 invested for 5 years at 3.1% APR, compounded monthly. A = P(1 + r/n)nt A = $5000(1 + 0.031/12)12×5 A = $5837.12 The interest is the amount earned beyond the original principal, P. I = A – P I = $5837.12 – $5000 I = $837.12 Applied Mathematics, 2nd Ed, Copyright 2018, Matovina & Yates