Compound interest is interest calculated not only on the original principal, but also on any interest that has already been earned.

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1 Section 10.2: Compound Interest Hmk: 1-26 (will not ask) (will ask). For example: 29, 31, 33, 39, 41, 45, 47, 51 (multi-step), 55, 59, 61, 69, 71, 65, 89. If setting up is hard just set up! If calculating is hard, answer! 1. Formulas: ( A = P 1 + r ) nt n ( r e = 1 + n) r n 1 Note the following: n - number of compounding periods a year r e - effective rate. Information/Definitions: Compound interest is interest calculated not only on the original principal, but also on any interest that has already been earned. The frequency with which the interest is compounded is called the compounding period. Annual: 1 Semiannual: 2 Quarterly: 4 Monthly: 12 Weekly: 52 Daily: 360 In calculations that involve compound interest, the sum of the principal and the interest that has been added to it is called the compound amount, or future value. The present value of an investment is the original principal invested, or the value of the investment before it earns any interest. Inflation is an economic condition during which there are increases in the costs of goods and services. This is expressed as a percent. The Rule of 72 states that the number of years for prices to double is approximately equal to 72 divided by the annual inflation rate. When interest is compounded, the annual rate of interest is called the nominal rate. The effective rate is the simple interest rate that would yield the same amount of interest after 1 year. (When a bank says 7% annual interest rate compounded daily and yielding 7.25% this means the nominal interest rate is 7% and effective rate is 7.25%.) 1

2 2. Example: Suppose you deposit $1000 in an account earning 5% interest, compounded annually. How much do you have at the end of 3 years? First Year: A = 1000 (1 + (0.05)(1)) = 1050 Second Year: Third Year: A = 1050 (1 + (0.05)(1)) = A = (1 + (0.05)(1)) = Notice that the first year you are only earning interest on $1000, but the second year, you are earning interest on $1050. You earn more interest as each year passes! Note, if the above example has interest compounded quarterly, you will end up with $ in the account after the first year, earning more interest. This is because after 3 months you earn interest on your $1000, which amounts to $ The second quarter you earn interest on both $1000 and $ Compound Interest Formula: Suppose interest is compounded annually. First year: A = P (1 + r) Second year: Third year: A = ( P (1 + r) ) (1 + r) = P (1 + r) 2 A = ( P (1 + r) 2) (1 + r) = P (1 + r) 3 4. You deposit $2000 in an account earning 4% interest, compounded monthly. How much is in the account at the end of 6 months? 5. Calculate the compound amount when $4000 is deposited in an account earning 6% interest, compounded monthly, for 2 years. 2

3 6. Suppose you got a gift from a generous relative of $2500, which is put into an account that earns 9% compounded weekly, and cannot take any money out of the account for 10 more years. How much money will you end up having, when you finally can take money out? How much interest did you earn during those 10 years you waited so patiently? 7. Suppose I want to go on an European vacation with my family in 5 years, and assume it will cost us a total of $20,000. If I put money into an account that earns 9% compounded semiannually, how much should I put now, in order to have enough? 8. Suppose you earn $35,000 annually, today. How much should you earn, with inflation, in 20 years, if you assume a 6% inflation rate? 3

4 9. In the early 1970s, students borrowed an average of $2000 to cover the entire cost of their educations. If there is an average inflation rate of 3.97% per year between 1970 and 2018, how much would this be equivalent to borrowing today? 10. Today, average student loan debt is over $15,000 at public colleges and over $17,000 at private colleges. Should we feel sorry for students today, compared to students in the 70 s? Why or why not? 11. Suppose you purchase an insurance policy in 2010 that will provide you with $500,000 when you retire in 40 years. Assuming an annual inflation rate of 7%, what will be the purchasing power of half a million dollars in 2050? 12. A bank offers a certificate of deposit at an annual interest rate of 4%, compounded quarterly. Find the effective rate. Round to the nearest hundredth of a percent. 4

5 13. One bank advertises an interest rate of 5.5%, compounded quarterly, on a certificate of deposit. Another bank advertises an interest rate of 5.25%, compounded monthly. Which investment has the higher annual yield? 14. You deposit $7500 in a two-year certificate of deposit (CD) earning 9.9% interest, compounded daily. At the end of the two years, you reinvest the compound amount plus an additional $7500 in another two-year CD. The interest rate on the second CD is 10.8%, compounded daily Waht is the compound amount when the second CD matures? 5