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.
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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.
$ 500 is deposited in a savings account that earns 5.25 % annual interest compounded annually.
We can immediately identify P as 500. Also, the annual interest rate, written as a decimal number, is 0.0525. Finally, since the interest is compounded annually, we have that n= 1. Let's substitute these values into the formula and simplify.
