A staple in algebra classes, the PERT formula sometimes seems to be nothing more than a cruel invention intended to test a student's knowledge of exponential and logarithmic skills. However, anyone looking to plan their finances should be familiar with it because it provides an invaluable tool for calculating compound interest. Whether you use it to figure out how much money you will have accumulated after a certain point in time, or wish to know how much or how long to invest, it will help you make these basic calculations.

- Skill level:
- Moderate

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### Things you need

- Calculator with an "e" and an "ln" button
- Writing utensil
- Paper

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## Instructions

- 1
Write down the formula A = Pe^rt and remind yourself what each of the letters represents. "A" is the amount of money that you will take out in the end, or the total amount of money that you will end up paying for a loan. "P" is the initial investment or loan amount. The letter "e" is a special number that can be rounded to 2.71, while "r" stands for rate and "t" stands for time (in years).

- 2
Rewrite the formula and replace the P with the amount of money that you want to put in a savings account that is compounded continuously or with the amount you are borrowing on continuously compounded interest. Replace e with 2.71 and t with the number of years you plan to leave the money in the account. For example, if you are putting £3,250 into an account for 10 years, the formula would look like this: A = 5,000(2.71)^(10r)

- 3
Change the interest rate from a percentage to a decimal and write it in as r. If the interest rate were 2.5 per cent, you would write out the formula as A = 5,000(2.71)^(10*.025).

- 4
Copy the right side of the formula into your calculator, if you are using one that recognises order of operations, and hit "Enter." If it does not recognise the order of operations, multiply r by t first. Then raise 2.71 to this answer as a power. Finally, multiply what you get with P.

The answer for A represents the amount of money you will have after the given amount of time or the amount of money you will have to pay back.

- 5
Find the amount you need to invest if you want to reach a certain amount of money by giving A a value instead of P. Once you have multiplied t and r and raised e to that power, divide A by this amount to figure out how much you need to invest. For instance, if you want to have £13,000 in 15 years from an account with 3.2 per cent interest compounded continuously, the formula would read: 20,000 = P(2.71)^(.032*15), which would simplify to 20,000 = 1.616P. You would then divide 20,000 by 1.616 to find that you need to invest £8,044.1.

- 1
Place all of the values into the formula A = Pe^rt, filling in both A and P but leaving t blank. For example, if you want to have £65,000 by investing £32,500 in an account with 2.7 per cent interest compounded continuously, you would write it like this: 100,000 = 50,000(2.71)^(.027t).

- 2
Divide A by P on the left side. In the example, you would end up with 2 = (2.71)^(.027t). Then, write "ln" in front of both sides. This stands for "natural log" and will let you solve for t even though it is an exponent. For instance, you would right ln(2) = ln[(2.71)^(.027t)].

- 3
Calculate the natural log on the left side with the calculator. In this case, you would hit "ln" of 2, then close the parentheses and push "Enter" to get the answer. Write this down on the left side.

- 4
Use the exponent rule to take .027t and move it down in front of the ln on the right side as a coefficient. At this point, the formula would look like this: .693 = .027t (ln2.71). Because ln of e = 1, you can rewrite the problem without the natural log on the right side like this: .693 = .027t.

- 5
Divide the number on the left by the number on the right to solve for t. In this case, you would get t = 25.67, which means it will take almost 26 years to earn the total interest that you want.

#### Tips and warnings

- Change percentages to decimals by lining up the ones digit with the hundredths digit. For example, 15.5 per cent would be .155, and .4 per cent would be .004.
- Do not forget to put the parentheses in the proper place when you enter the numbers in the calculator.