A credit union client deposits $2,100 in an account earning 4.5% interest, compounded quarterly. What will the balance of the account be at the end of 22 years?

Answer 1

Since this is a compound interest problem, we will use the formula A = P ( 1 + r/n) ^nt where A = the final amount, P = the initial deposit, r = the annual interest rate, n = the # of times the interest is compounded per year, and t = the # of years. Plugging in the given values, we have A = 2100( 1 + .045/4)^{4 · 22}.

Since the unknown is already isolated on the left side, we will simply work the arithmetic on the right side of the equation to find the value of A. We need to follow Order of Operations on this, so we start inside the parentheses. 1 + .045/4 becomes 1.01125. Now we raise this to the 88th power ( because of 4 · 22), so 1.01125⁸⁸ becomes 2.6764. Now we multiply this by 2100 and we get 5,620.44, so this will be our amount at the end of 22 years, given the specific conditions we are working with.