James invests 3000 dollars at a two percent interest rate per year, compounded quarterly. Find the balance after 10 years.
The good news for us is we know the compound interest formula. It looks like this. We have the balance, the principal or the amount you initially invested, the 𝑟 is your interest rate written as a decimal, the 𝑛 that shows up twice is the number of times interest is compounded per year. And our 𝑡 stands for time in years. What we’ll do now is we’ll plug in all the information that we know.
We know that James invested 3000 dollars. We also know that his interest rate is two percent. But remember that we have to write this two percent as a decimal. We know that two percent equals two over 100 if it’s written as a fraction. And two hundredths written as a decimal looks like this: 0.02. So we put that into our formula. Our interest is compounded quarterly. There are four quarters per year. So we divide by four. And we have an 𝑛 in our exponents. So we’ll put the four, for compounded quarterly, in the exponents. We wanna check the balance after 10 years. So our 𝑡, our time in years, equals 10.
Let’s reduce this problem a little bit so that we can solve it. Bring down the 3000. Bring down the one plus. Two hundredths divided by four equals 0.005. And four times 10 equals 40. So we’re gonna be using an exponent of 40. From this stage, we can enter everything in this problem into our calculator, exactly as it’s written here.
Our calculator gives us the answer 3662.382709. But remember, we’re talking about money. And money needs to be rounded to the nearest cent. The rest of the decimal point doesn’t matter. We look at the two to determine if the eight will round up to nine or stay the same. Two is less than five so our eight stays the same.
James’s total balance after 10 years is 3662 dollars and 38 cents. So he has earned 662 dollars and 38 cents in interest.