Percentage lost

Question

I need a formula to calculate something like this

if I have 5000 dollars and loose 5% of it per DAY. How many days is it going to take to have 10 dollars left in my pockets.

Answer 1

In general - starting out with $\$X$, if you lose $x\%$ everyday, then after $1$ day, you'll have $(100-x)\%$. So, after $n$ days, if you have $Y$ dollars, then you'll have to solve: $$Y=\left(1-\dfrac{x}{100}\right)^nX$$ In this case, you have $n\approx121.158$ days.

Answer 2

• Day 1: $5000$
• Day 2: $5000 - 0.05 \times 5000 = 5000 \times 0.95 = 4750$
• Day 3: $4750 - 0.05 \times 4750 = 4750 \times 0.95 = 5000 \times 0.95 \times 0.95 = 5000 \times 0.95^2$
• $\ldots$
• Day n: $5000 \times 0.95^n$

Now, solve:

$$5000 \times 0.95^n = 10 \implies n = 121.158$$