Week 1-Participation Discussion-Math 012 12) You borrow S25000 at 12.25% interest compounded monthly. If you are unable to make any payments the rst year, how much do you owe, excluding penalties? Sample: Functions - Compound Interest Objective: Calculate nal account balances using the formulas for compound and continuous interest. An application of exponential functions is compound interest. When money is invested in an account (or given out on loan) a certain amount is added to the balance. This money added to the balance is called interest. Once that interest is added to the balance, it will earn more interest during the next compounding period. This idea of earning interest on interest is called compound interest. For example, if you invest S100 at 10% interest compounded annually, after one year you will earn S10 in interest, giving you a new balance of S110. The next year you will earn another 10% or S11, giving you a new balance of S121. The third year you will earn another 10% or S12.10, giving you a new balance of S133.10. This pattern will continue each year until you close the account. There are several ways interest can be paid. The rst way, as described above, is compounded annually. In this model the interest is paid once per year. But interest can be compounded more often. Some common compounds include compounded semi-annually (twice per year), quarterly (four times per year, such as quarterly taxes), monthly (12 times per year, such as a savings account), weekly (52 times per year), or even daily (365 times per year, such as some student loans). When interest is compounded in any of these ways we can calculate the balance after any amount of time using the following formula: Compound Interest Formula: A =P1+ r / nt A =Final Amount P =Principle (starting balance) r =Interest rate (as a decimal) n=number of compounds per year t=time (in years)