Simple and Compound Interest
Simple Interest Formula: Compound Interest Formula:
(Interest is only earned on principal) (interest is earned on principal and any accumulated interest)
I = PRT A = P( 1 + r/n )^nt
I = amount of interest earned A = amount in the account, including interest and principal
P = principal or amount of loan P = principal or amount of loan or investment
R = annual interest rate, decimal form r = annual interest rate, decimal form
T = time, in years n = number of compounds per year
t = time, in years
Use the given formulas to answer the following questions.
If $6000 is deposited into an account earning simple interest at an annual interest rate of 3% for 5 years, how much interest was earned?
For the situation in question #1, how much money is now in the account?
Solve the simple interest formula, I = PRT, for P.
(Do NOT substitute any numbers for the variables. Leave all variables, and just isolate P.)
If $6000 is deposited into an account earning compound interest at an annual interest rate of 3% for 5 years, and it is compounded quarterly (thus 4 times per year), how much money is in the account at the end of the 5 years?
For problem #4, how much interest was earned?
Sara would like to go on a vacation in 5 years and she expects her total costs to be $2500. If she invests $1900 into a savings account for those 5 years at 6.5% interest, compounding semi-annually, will she be able to go on vacation?
Compare and contrast the simple and compound interest formulas. Which one of the following statements is correct?
Simple interest and compound interest formulas both yield principal plus interest, so you must subtract the principal to get the amount of interest.
Simple interest formula yields principal plus interest, so you must subtract the principal to get the amount of interest; Compound interest formula yields only interest, which you must add to the principal to get the final amount.
Simple interest formula yields only interest, which you must add to the principal to get the final amount; Compound interest formula yields principal plus interest, so you must subtract the principal to get the amount of interest.
Simple interest and compound interest formulas both yield only interest, which you must add to the principal to get the final amount.
Compare the interest earned from #1 (where simple interest was used) to #5 (where compound interest was used). The principal, annual interest rate, and time were all the same; the only difference was that for #5, interest was compounded quarterly. Does the difference in interest earned make sense? Select one of the following statements.
No, because more money should have been earned through simple interest than compound interest.
Yes, because more money was earned through simple interest. For simple interest you earn interest on interest, not just on the amount of principal.
No, because more money was earned through simple interest. For simple interest you earn interest on interest, not just on the amount of principal.
Yes, because more money was earned when compounded quarterly. For compound interest you earn interest on interest, not just on the amount of principal.
Find the price of a car online that you would like to purchase. (This can be as realistic as possible, a car that you’ve always dreamed of owning, or just a random car that you see online.) How much does it cost?
Use the simple interest formula to determine what your monthly payment would be if you take a loan out to pay for the car. Assume that you do not have a down payment, you are taking the loan out for 5 years, and the annual interest rate is 7%. (You do NOT have to include any tax.)
Some questions to answer to help you solve this problem:
What is the total amount that you will need to repay?
How many months will you be paying for the car?
How much per month will you need to pay?