As a savings plan for college, when their son Bob was born, the Wilburs deposited $10,000 in an account paying 8% compounded annually. How much will the account be worth when Bob is 18 years old?
1.08^18 = 4
so
$40,000
To determine how much the account will be worth when Bob is 18 years old, we need to calculate the future value of the initial deposit compounded annually at an 8% interest rate. The formula to calculate the future value of an investment compounded annually is:
Future Value = Present Value * (1 + Interest Rate)^Number of Periods
In this case, the present value is $10,000, the interest rate is 8% (or 0.08 as a decimal), and the number of periods is 18 years. Plugging these values into the formula, we get:
Future Value = $10,000 * (1 + 0.08)^18
To calculate this, we can use a calculator or a spreadsheet program.
Alternatively, we can break down the calculation step by step.
First, let's calculate the interest for one year:
Interest = Present Value * Interest Rate
Interest = $10,000 * 0.08
Interest = $800
Now, let's calculate the future value after one year:
Future Value_1 = Present Value + Interest
Future Value_1 = $10,000 + $800
Future Value_1 = $10,800
Next, let's calculate the future value after two years:
Future Value_2 = Future Value_1 * (1 + Interest Rate)
Future Value_2 = $10,800 * (1 + 0.08)
Future Value_2 = $10,800 * 1.08
Future Value_2 = $11,664
Continuing this process, we can calculate the future value after 18 years:
Future Value_18 = Future Value_17 * (1 + Interest Rate)
Future Value_18 = $11,664 * (1 + 0.08)
Future Value_18 = $11,664 * 1.08
Future Value_18 ≈ $25,208.39
Therefore, the account will be worth approximately $25,208.39 when Bob is 18 years old.