You have just deposited X dollars in your bank account that pays interest of 6 percent p.a. you discover that at the end of one year you have $19,935 in the account. What was X, that is, the amount of money that you deposited today?
Answer: $18,806.60
Can anyone provide me the steps to solve this problem? I mean I know I can just keep plugging in number to my calculator, but there has to be a formula for this!
1.06x = 19,935
Yes, there is a formula to solve this problem called the future value formula. The formula is:
Future Value = Principal (1 + interest rate)^time
In this case, the future value is given as $19,935, the interest rate is 6% (or 0.06 as a decimal), and the time is 1 year. We need to find the principal, which is the amount of money you deposited initially.
To solve for the principal, we rearrange the formula:
Principal = Future Value / (1 + interest rate)^time
Substituting in the given values:
Principal = $19,935 / (1 + 0.06)^1
Principal = $19,935 / (1.06)^1
Principal = $19,935 / 1.06
Principal = $18,806.60
Therefore, the amount of money you deposited today (X) is $18,806.60.