A few terms you need to know for this section:

Principal: The initial amount that is invested.

Simple Interest: Interest is paid on the principal only.

Compound Interest: Interest paid on BOTH the principal and on all interest that has been earned up to that point.

SIMPLE
Interest / COMPOUND
Interest
You deposit $1000 in a bank that paysa simple interest of 5% annually. How much do you have in the bank after….
one year:
two years:
three years: / You deposit $1000 in a bank that pays 5% interest compounded annually. How much do you have in the bank after….
one year:
two years:
three years:

1) While most banks pay compound interest, bonds usually pay simple interest. Which is the better investment: investing $1000 in a savings bond for 5 years that pays a simple interest rate of 10% per year, or investing $1000 in a bank for 5 years that pays 9% annual interest rate, compounded annually?

End of Year /

Simple Interest


Interest New Balance /

Compound Interest


Interest New Balance
1
2
3
4
5

THE COMPOUND INTEREST FORMULA

(for interest paid once a year)

A = Accumulated balance after Y years (also called future value (FV))
P = Starting principal (also called present value (PV))
APR = Annual percentage rate Express it as a decimal!!!
Y = Number of years
Note: It is very important that you do not round in the middle of the problem!!!

2) You invest $25,000 in an account that has an APR (annual interest rate) of 8% compounded annually. What’s the balance in your account after 10 years?

3) Your friend invests $25,000 in an account that earns 8% annually in simple interest. What’s the balance in your friend’s account after 10 years?

4) You invest $100 in two accounts that each pay an interest rate of 10% per year. One account pays simple interest and one account pays compound interest. Make a table that shows the growth of each account over a 5-year period. Use the compound interest formula to verify the result in the table for the

compound interest case.

End of Year /

Simple Interest

Interest New Balance /

Compound Interest

Interest New Balance
1
2
3
4
5

5) On July 18, 1461, King Edward IV of England borrowed the modern equivalent of $384 from New College of Oxford. The King soon paid back $160, but never repaid the remaining $224. The debt was forgotten for 535 years. Upon its rediscovery in 1996, a New College administrator wrote to the Queen of England asking for repayment with interest. Assuming an interest rate of 4% per year, he calculated that the college was owed $290 billion. Is this possible????? How was the interest calculated????

a) Calculate the amount due to New College if the interest is computed as simple interest and as interest that’s compounded annually.

b) What if the interest rate was 2% per year?

6) How much will you need to deposit today into a bank with an APR of 5.4%, compounded annually, if you want to have $50,000 in the bank in 20 years?

THE COMPOUND INTEREST FORMULA

(for interest paid “n” times per year)

A = Accumulated balance after Y years (also called future value (FV))
P = Starting principal (also called present value (PV))
APR = Annual percentage rate Express it as a decimal!!!
Y = Number of years
n = Number of compounding periods per year
Note: It is very important that you do not round in the middle of the problem!!!

7a) You deposit $5000 in a bank that pays an APR of 3%, compounded monthly. How much money will you have after 5 years? b) How much would you have, if instead, the interest was paid quarterly?

8) Your grandfather put $100 under his mattress 50 years ago. If he had instead invested it in a bank paying 3.5% interest, compounded quarterly,then how much would it be worth now?

9) How much must you deposit today into an account with an APR of 5.2%, compounded daily, in order to have $100,000 in 25 years?

Annual Percentage Yield (APY):

  • Is the actual percentage by which a balance increases in one year.
  • It is equal to the APR if interest is compounded annually.
  • It is greater than the APR if interest is compounded more than once a year.
  • The APY does not depend on the starting principal.
  • The APY is sometimes also called the effective yield or simply the yield.

10) Find the APY for a bank that offers an APR of 4.5% compounded quarterly.

11) You deposit $5000 into an account with APR = 8%. Find the annual percentage yield with monthly compounding and with daily compounding.

THE COMPOUND INTEREST FORMULA

(for interest paid continuously)

A = Accumulated balance after Y years (also called future value (FV))
P = Starting principal (also called present value (PV))
APR = Annual percentage rate Express it as a decimal!!!
Y = Number of years
e  2.71828 (use the “e” button on your calculator)i

12) You deposit $100 in an account with an APR of 8%,compounded continuously. How much will you have after 20 years?

13) You deposit $20,000 in a bank with an APR of 3.4%, compounded continuously. What will be your balance after 1, 10, and 15 years? What’s the APY?