If I have 10.000 dollars, and make 1% profit per day. How much do I have after a year? And what is the formula?

Question

finance math

Answer 1

Hello, thank you for taking the time to post your question!

The underlying formula that you want to use to solve this one is

A = P(1 + r)^t , where A is the final amount, P is the initial amount invested (10,000), r is the daily profit or return (0.01), and t is the number of days (365)

When I plug those values in and simplify I get

A = 10000(1 + 0.01)^365

A = $377,834.34

So at the end of year you would have close to $400,000, which shows you how magical that compound interest can be when it’s working in your favor

I hope that helps get you moving in the right direction! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

The definition of a profit is the amount of money gained and is often thought of in percentages. In this question, you start with a certain amount of money, called your principal, and then make 1% profits on your principal every day for a year. The simple equation for profits made is F = P + (P x i) where F is the total earned, P is the principal (starting amount of money),  and i is the percent profits written as a decimal. If we were to calculate profits for just one day, and P = $10,000 and i = 0.01, then F = $10,000 + $10,000*0.01) = $10,000 + $100 = $10,100.

 

However, our question is more tricky than this simple calculation since the principal P changes every single day for 365 days. This is because you're not pocketing those profits and starting over with $10,000 each day. Instead, you are re-investing the total (principal + profit) from Day 1 as the principal for Day 2, then the total from Day 2 as the principal for Day 3, etc for 365 days. Fortunately for us, i (0.01) stays the same the whole time.

 

Imagine if we start to calculate the profits made day by day. On Day 1, since $10,000 x 0.01 = $100, your new principal is $10,100 (as we determined above). On Day 2, the starting principal is $10,100 and the profit is still 0.01, so at the end of Day 2 you have $10,100 + ($10,100*0.01) = $10,201. On Day 3, the starting principal is $10,201 and at the end of Day 3 you have $10,201 + ($10,201*0.01) = $10,303.01. 

 

There has to be a simpler way of calculating what your total will be after 365 days. Lucky for us, there is! 

 

F = P(1 + i)^n

 

Again, F is the total value, P is the starting principal, and i is the profit percentage. The new value, n, is the total number of days you are gaining profits. An important thing to remember about using equations like this is the order of operations. Remember PEMDAS: parentheses (), exponent ^, multiplication x, division /, addition +, and subtraction -.

 

First try using n = 1 or n = 3 in this equation to see how the totals compare to the day-by-day totals we calculated above (and to make sure you're using the right order of operations). Then use n = 365 to answer the original question. I'm not going to just give the answer here, but here's a hint: 1% a day may not sound like much, but it can mean making a TON of money after a whole year!