Compound interest
Big idea- Compound interest is the way maost banks and other savings institutions pay savers who put their money into their accounts.
How is intersest calculated
An important application of exponets and powers occurs with savings accounts. When you save money,you can choose where to put it. Of cousre, you can keep it home, but banks, savings, and loan associations, and credit unions will pay you to let them hold your money for you. The amount you give them at the start is called the principal. The amount they pay is called interest.
Interest is always a percent of the principal. The percent that the money per yar is called annual yield.
example 1
If the account is left alone, how much money will be in it at the end of a year?
solution
Total= principal +interest ( 4% of principal)
= P + 0.04
= ( 1 + 0.04)P =1.04P
You will have 1.04P, or 104% of the principal
solution
Total= principal +interest ( 4% of principal)
= P + 0.04
= ( 1 + 0.04)P =1.04P
You will have 1.04P, or 104% of the principal
compound interest
When the year is up, will have extra money in it because of the interest it earned. If the money is left n the account, then at he end of second year, the bank will pay interest on all the money that is now in the account ( the original principal and the first year's interest). This leads to compound interest, which means that he interest earns interest.
Compound interest formula- if a principal p an annual yeild of r, then after t years there will be a total amont a, where a = p(1+r)^t
vocab
power- A number expression in the form x^n
nth power- The number x^n is the nth power of x.
base- The number xin the power x^n.
exponet-The number n in the power x^n.
principal- Money deposited in an account.
interest- The amount that a bank or other financial institution pays on money in an account, based on a percentageof the principal.
annual yeild- The percent of interest that money on depoist earns per year.
compund interest- The bank pays on on the principal and earned interest in an account.
nth power- The number x^n is the nth power of x.
base- The number xin the power x^n.
exponet-The number n in the power x^n.
principal- Money deposited in an account.
interest- The amount that a bank or other financial institution pays on money in an account, based on a percentageof the principal.
annual yeild- The percent of interest that money on depoist earns per year.
compund interest- The bank pays on on the principal and earned interest in an account.