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Mark borrows 10 dollars from Emily with a simple interest rate of 15% everyday. What is the least integer number of days after which Mark will have to pay her back at least twice as much as he borrowed?

 May 12, 2024
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Interest rate per day is 15% / 100 = 0.15

 

The amount Mark owes increases by 0.15 each day.

 

We want to find the number of days needed to reach an amount that is at least twice what he borrowed (which is 10 x 2 = $20).

 

Let's set up a table to track the daily increase:

 

DayAmount Owed

 

1$10 + $0.15 = $10.15

 

2$10.15 + $0.15 = $10.30

 

3$10.30 + $0.15 = $10.45

 

4$10.45 + $0.15 = $10.60

 

5$10.60 + $0.15 = $10.75

 

We can see that after 5 days, the amount owed is $10.75, which is still less than $20.

 

One more day of interest will bring the total to $10.75 + $0.15 = $10.90.

 

Therefore, it will take Mark at least 5​ days to pay back at least twice the amount he borrowed.

 May 13, 2024

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