Transcript Slide 1
Interest MATH 102 Contemporary Math S. Rook Overview • Section 9.2 in the textbook: – Simple interest – Compound interest Simple Interest Simple Interest • Interest: amount paid in return for borrowing somebody else’s money – e.g. Banks pay you to use your money; You pay credit card companies when you make a purchase on a credit card • Simple Interest: given a starting principal P, a rate of growth r, an amount of time t in years: I = Prt – Note that interest is paid only on the initial principal Simple Interest (Continued) • Future amount: the total amount of money owed to a borrower over a time period of t years: A = P + I where I is the total amount of simple interest – What is the formula for simple interest? – Simplifies to A = P(1 + rt) – There are four variables in the future amount formula: • Given any three, we can solve for the fourth using Algebra Simple Interest (Example) Ex 1: Suppose that $12,000 is placed into an account which pays 5% simple interest annually. If the money is left alone in the account for 8 years: a) Calculate the interest earned (round to the next highest cent) b) Find the total amount in the account Simple Interest (Example) Ex 2: Suppose you wished to save up $10,000 in 10 years by placing money into a CD which pays 4.5% simple interest. How much money would you need to invest in the account to meet the goal (round to the next highest cent)? Compound Interest Compound Interest • Recall that simple interest only pays interest on the initial principal – In the real world, interest is compounded (computed) on the current total amount (principal along with interest) • Interest is compounded n times per year. n is known as the compounding period r⁄ n interest is added to the current amount each compounding period – Common compounding periods: annually (1), biannually (2), quarterly (4), monthly (12) Compound Interest (Continued) • Formula for compound interest: A P1 r n – Note that this formula is slightly nt different from the one given in the book • Book says to let n = # of compounding periods, but it is easier to compute nt • Compound interest formula has four variables – Given the value of any three variables, we can solve for the fourth – Will only be asked to solve for A and P for compound interest Compound Interest (Example) Ex 3: Calculate (to the nearest cent) the amount in the account (round to the next highest cent): a) $5000 invested at 5% compounded annually over 5 years. b) $4000 invested at 8% compounded quarterly over 2 years. c) $20,000 invested at 10% compounded monthly over 4 years. Compound Interest (Example) Ex 4: A mother wishes to establish a $30,000 college fund for her child at the end of 15 years. How much should she initially deposit into an account with a 6% interest rate compounded twice a year to achieve this (round to the next highest cent)? Compound Interest (Example) Ex 5: Suppose you take out a loan for 10 years at a rate of 8.5% compounded monthly. If the total amount to be paid back at the end of the 10 years is $25,000: a) How much did you borrow (round to the next highest cent)? b) How much interest do you pay? Summary • After studying these slides, you should know how to do the following: – Calculate values using the simple interest formula – Calculate values using the compound interest formula • Additional Practice: – See problems in Section 9.2 • Next Lesson: – Consumer Loans (Section 9.3)