COMPOUND INTEREST Since this section involves what can happen to your money, it should be of INTEREST to you!

IMPLE INTEREST FORMULA Interest paid Principal (Amount of money invested or borrowed) annual interest rate (as a decimal) time (in years) I = Prt

If you invested $ in an account that paid simple interest, find how long you’d need to leave it in at 4% interest to make $ = (200)(0.04)t 1.25 yrs = t Typically interest is NOT simple interest but is paid semi- annually (twice a year), quarterly (4 times per year), monthly (12 times per year), or even daily (365 times per year). enter in formula as a decimal

COMPOUND INTEREST FORMULA amount at the end Principal (amount at start) annual interest rate (as a decimal) time (in years) number of times per year that interest in compounded

(2) Effective rate of interest is the equivalent annual simple rate of interest that would yield the same amount as that made compounding. This is found by finding the interest made when compounded and subbing that in the simple interest formula and solving for rate. Find the effective rate of interest for the problem above. The interest made was $ Use the simple interest formula and solve for r to get the effective rate of interest. I = Prt 85.83=(500)r(2) r = = 8.583% Find the amount that results from $500 invested at 8% compounded quarterly after a period of 2 years.

CONTINUOUS INTEREST FORMULA Amount at the end Principal annual interest rate (as a decimal) time natural base (on calculator)

Find the amount that results from $40 invested at 7% compounded continuously after a period of 3 years. 40 (.07)(3) A = $49.35 Now punch buttons in your calculator. Make sure you put parenthesis around the entire exponent on e.

If you want to know the amount to invest now to obtain a certain amount with a given interest rate for a given time, you’ll want to take the interest equation and solve for P. This formula is called the Present Value. (It can easily be obtained from the other formula so you just need to memorize the simple, compound and continuous interest formulas and you can solve for P if necessary). You can divide both sides by the stuff in the parenthesis to get P alone. We can represent this division with a negative exponent.

Similarly if you have continuously compounding interest you can find the Present Value by solving for P.