The formula that gives the balance y of an account earning compound interest is y=P( 1+ rn )^(nt), where P is the principal, r is the annual interest rate, t is the time in years, and n is the number of times the interest is compounded in one year.
y=2000(1.0125)^(4t)
Practice makes perfect
Compound interest is the interest earned on the principal and on previously earned interest. Let's recall the formula that gives the balance y of an account earning compound interest.
y= P( 1+r/n )^(nt)
In this formula P is the principal or initial amount, r is the annual interest rate written in decimal form, t is the time in years, and n is the number of times the interest is compounded in one year. Let's pay close attention to the given exercise.
We can immediately identify P as 2000. Also, the annual interest rate, written as a decimal number, is 0.05. Finally, since the interest is compounded quarterly, we have that n= 4. Let's substitute these values into the formula and simplify.
