Hello! The formula for finding compound interest is A = P(1 + r/n)^nt. That means divide the rate by the amount of times compounded per year, add 1 into that, with the exponent, combine how many times it would be compounded overall and then put the percentage up into a power and multiply by the principal. In other words. r = rate, n = number of times compounded each year, t = time, and P = principal. Principal is the initial amount in the account. It's a bit confusing, but let's do this step by step. If you know the solve this by step, it will help you later on.
How to solve this problem:
First off, to solve this and for compound interest problems in general, you will need a calculator. Okay, so the interest is compounded monthly at 4%, which means it will be compounded 12 times per year. Let's do the parenthesis first. do 4% (0.04) divided by 12 to get 0.003333333. You should have a number like this shown on calculator. Now, add 1 to it to get 1.003333333. Leave that number on your calculator. Now, with a scrap sheet of paper or a separate calculator, let's solve to see what number our exponent is. We use the values of n and t. In this case, n = 12, and t = 13. Multiply both numbers together to get our exponent. 12 * 13 is 156. So you will multiply 1.003333333 to the 156th power. Now, on your calculator with the long decimal, raise it up to the 156th power. When you do that, you should get a decimal with the digits 1.680573752. Leave that decimal on your calculator. Now, multiply that by the principal (12,000). When you do, you get 20,166.88502 or 20,166.89 when rounded to the nearest hundredth. At the end of 13 years, Marcus will receive $20,166.89.
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