Simple and Compound Interest
Calculating interest, balances, rates, and time
Simple and Compound Interest
Calculating interest, balances, rates, and time
Math - Grade 6-8
- 1
Lena deposits $200 in an account that earns 5% simple interest each year. How much interest will she earn after 3 years?
Use the formula I = P x r x t.
Lena will earn $30 in simple interest because I = 200 x 0.05 x 3 = 30. - 2
A savings account has a principal of $450 and earns 4% simple interest for 2 years. What is the total balance at the end of 2 years?
The simple interest is $36 because 450 x 0.04 x 2 = 36. The total balance is $486. - 3
Marcus earned $36 in simple interest on a principal of $300 after 3 years. What was the annual interest rate?
Solve I = P x r x t for r.
The annual interest rate was 4% because 36 = 300 x r x 3, so r = 36 divided by 900 = 0.04. - 4
A loan of $600 earns $72 in simple interest at an annual rate of 6%. How many years did it take to earn that interest?
It took 2 years because 72 = 600 x 0.06 x t, and 72 divided by 36 equals 2. - 5
In an interest problem, what does the principal represent?
The principal is the starting amount of money that is invested, saved, or borrowed before interest is added. - 6
A $1,000 investment earns 5% interest compounded annually for 2 years. What is the final balance?
For compound interest, each year's interest is added before the next year's interest is calculated.
The final balance is $1,102.50. After year 1 the balance is $1,050, and after year 2 it is 1,050 x 1.05 = $1,102.50. - 7
An account starts with $800 and earns 10% interest compounded annually. Find the balance after year 1, year 2, and year 3.
The balances are $880 after year 1, $968 after year 2, and $1,064.80 after year 3. - 8
Compare $500 invested at 8% simple interest for 3 years with $500 invested at 8% interest compounded annually for 3 years. Which has the larger balance, and by how much?
Calculate the simple interest balance first, then multiply by 1.08 for each year in the compound interest account.
The compound interest account has the larger balance. The simple interest balance is $620, the compound interest balance is $629.86, and the difference is $9.86. - 9
A bank compounds $300 annually at a rate of 3% for 4 years. What is the final balance rounded to the nearest cent?
Multiply the balance by 1.03 once for each year.
The final balance is $337.65 because 300 x 1.03 x 1.03 x 1.03 x 1.03 = 337.65 when rounded to the nearest cent. - 10
Nia can invest $1,200 for 2 years. Option A earns 6% simple interest. Option B earns 5.5% interest compounded annually. Which option gives her more money after 2 years?
Do not choose only by the interest rate. Calculate the ending balance for each option.
Option A gives her more money. Option A ends with $1,344, while Option B ends with $1,335.63. - 11
A credit union gives a simple interest loan of $900 at an annual rate of 7% for 1.5 years. How much interest will be paid?
The interest paid will be $94.50 because 900 x 0.07 x 1.5 = 94.50. - 12
An account earned $40 in simple interest at a rate of 5% per year for 2 years. What was the original principal?
Use I = P x r x t and solve for P.
The original principal was $400 because 40 = P x 0.05 x 2, so P = 40 divided by 0.10 = 400. - 13
Which type of interest usually grows faster over a long time, simple interest or compound interest? Explain why.
Think about whether interest is earned only on the original principal or also on earlier interest.
Compound interest usually grows faster over a long time because interest is added to the balance, and future interest is calculated on the new larger balance. - 14
Jay calculates the balance for $700 at 4% interest compounded annually for 3 years as 700 x (1 + 4)^3. What mistake did Jay make, and what expression should he use instead?
A percent must be written as a decimal before using it in a formula.
Jay used 4 instead of 0.04 for the interest rate. He should use 700 x (1 + 0.04)^3, which equals about $787.40. - 15
An account starts with $1,000 and earns 6% interest compounded annually. Find the balances for years 0, 1, 2, and 3. Then explain whether the yearly increase stays the same or changes.
The balances are $1,000 at year 0, $1,060 at year 1, $1,123.60 at year 2, and $1,191.02 at year 3. The yearly increase changes and gets larger because each year interest is calculated on a larger balance.