Compound Interest Practice

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Question 2
The total amount of money that we need to pay back after 3 years for a $3000 loan is $3993 . Find the compound interest rate of the loan.

Answer

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A. $2000
B. $3000
C. $4000
D. $5000
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Step by Step Solution 

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Step 1
We start with the compound interest formula:
compound interest formula

Where:   
  1. A is the total amount of money (including interest) after n years ($3993)
  2. P is the principal
  3. r is the interest rate per year (10 ÷ 100 = 0.1)
  4. n is the loan duration in year (3 years).
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Step 2
With A=3993, r=0.1 and n=3, we can substitute these values into the compound interest formula as shown below: 
using the compound interest formula to find the principal

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Step 3
Now we have, 1.331P = 3993. To find P, we need to remove 1.331. To do so, we divide both sides of the equation with 1.331. This is shown below:
dividing both sides with 1.331 to find P
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Step 4
Finally, we have P = $3000. Clearly, the answer is B.
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