One formula covers all of it: the rate gets divided by how often interest is added, and the exponent counts how many times that happens. Continuous compounding is the same formula pushed as far as it goes, which is where e comes from.
Round money to the nearest cent, times to the nearest tenth of a year and rates to the nearest hundredth of a percent.
Find the balance or interest compounded n times a year
$1300 is invested at 2% compounded semiannually to save for college. Find the balance after 6 years.$1464.87
$5000 is invested at 11% compounded annually for a term of 12 years. Find the interest earned.$12492.25
$6100 is invested at 15% compounded weekly (52 times a year) for a child's future. Find the balance after 29 years.$469668.33
$800 is invested at 3% compounded semiannually in a savings account and left for 5 years. Find the interest earned.$128.43
$4100 is invested at 9% compounded monthly in a certificate of deposit. Find the balance after 19 years.$22524.56
Solve continuous compounding problems
$2600 is invested at 10% compounded continuously for 13 years. Find the interest earned.$6940.17
How long does it take $500 to grow to $1500 at 6% compounded continuously?18.3 years
An account compounded continuously grows from $12,000 to $16,350 in 7 years. Find the annual interest rate, as a percent to the nearest hundredth.4.42%
$1500 compounded continuously grows to $5750 in 9 years. Find the annual rate, as a percent to the nearest hundredth.14.93%
$1500 is invested at 7% compounded continuously, and nothing is withdrawn. Find the balance after 9 years.$2816.42
How long does it take $6500 to grow to $9750 at 3% compounded continuously?13.5 years
$5700 is invested at 5% compounded continuously. How many years until it grows to $8550? Round to the nearest tenth of a year.8.1 years
How long does it take $9000 to grow to $18000 at 6% compounded continuously?11.6 years
A parent wants $29,000 for college in 10 years. How much should be invested now at 6% compounded continuously? Round to the nearest cent.$15,915.54
$3500 compounded continuously grows to $7250 in 14 years. Find the annual rate, as a percent to the nearest hundredth.5.20%
Find the deposit needed now
How much must be invested now at 7% compounded monthly to have $5000 in 8 years?$2860.70
How much must be invested now at 7% compounded annually to have $10000 in 11 years?$4750.93
How much must be invested now at 7% compounded quarterly to have $10000 in 18 years?$2867.62
How much must be invested now at 4% compounded continuously to have $8000 in 3 years?$7095.36
How much must be invested now at 4% compounded annually to have $10000 in 6 years?$7903.15
$1000 is invested at 5% compounded quarterly. Find the balance after 7 years.
The rate per quarter is 0.05 over 4.
There are 28 quarters.
1000 times 1.0125 to the 28th.
The answer is $1415.99.
Where students go wrong
Putting the yearly rate in without dividing it. Compounded monthly means one twelfth of the rate twelve times a year, not the whole rate twelve times, and the difference is enormous over twenty years.
Also called continuous compounding, interest formula or exponential growth.
What you can put on this worksheet
Compounded a set number of times a year
$1100 is invested at 5% compounded annually. Nothing is added or taken out for 8 years. Find the interest earned.→ $525.20
Compounded continuously
$1100 is invested at 5% compounded continuously. Nothing is added or taken out for 8 years. Find the interest earned.→ $541.01
How long it takes to double
How many years does it take money invested at 5% compounded semiannually to double?→ 14.0 years
The deposit needed now
How much must be invested now at 5% compounded annually to have $8000 in 16 years?→ $3664.89
Continuous compounding: the rate or the time
How long does it take $5500 to grow to $16500 at 7% compounded continuously?→ 15.7 years
Solve for the number of steps or the rate
A town of 59,000 people grows by 3.6% a year. After how many years does it have 70,413 people?→ 5 years
Questions about these worksheets
Yes. Every compound interest sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.
Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.
Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.
Precalculus is usually taken around 11th or 12th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.
Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.
That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the compound interest questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.
Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.
You pick from 6: compounded a set number of times a year, compounded continuously, how long it takes to double, the deposit needed now, continuous compounding: the rate or the time and solve for the number of steps or the rate. Tick as many as you want and set how many of each, or let it spread them evenly.
Putting the yearly rate in without dividing it. Compounded monthly means one twelfth of the rate twelve times a year, not the whole rate twelve times, and the difference is enormous over twenty years.