Question:
If Michael paid $3564 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$3300
Solution And Explanation
Solution
Given,
Amount (A) = $3564
Rate of Simple Interest (R) = 2%
Time (T) = 4 years
Thus, Principal (P) = ?
Method (1) Using Formula
Calculation of the Principal using forumula when Amount, Time and Rate of Simple Interest are given
Formula to find the Principal (P)
Amount (A) = Principal (P) + Principal (P) × Rate (R) × Time (T)
⇒ Amount (A) = Principal (P) [1 + Rate (R) × Time (T)]
⇒ A = P (1 + RT)
Using the formula to find the Amount (A), the fourth can be calculated if any three of A, P, R, and T are given
In the given question, we need to find the Principal (P)
Therefore, by substituting, Amount, Rate, and Time, in the formula A = P (1 + RT) we get
$3564 = P (1 + 2% × 4)
⇒ $3564 = P (1 + 2/100 × 4)
⇒ $3564 = P (1 + 2 × 4/100)
⇒ $3564 = P (1 + 8/100)
⇒ $3564 = P (100 + 8/100)
⇒ $3564 = P × 108/100
⇒ P × 108/100 = $3564
⇒ P = 3564/108/100
⇒ P = 3564 × 100/108
⇒ P = 3564 × 100/108
⇒ P = 356400/108
⇒ P = $3300
Thus, the sum borrowed (P) = $3300 Answer
Method (1) Using Unitary Method
Calculation of the Principal using unitary method when Amount, Time and Rate of Simple Interest are given
Calculation of the Simple Interest
Let, the principal = 100
Here, since rate of simple interest = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
Calculation of the Amount
Since, in the question, time = 4 years
So, we need to calculate the simple interest for the given time period, which is 4 years
Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year
= 4 × 2 = 8
Thus, simple interest for 4 years = 8
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 8 = 108
Calculation of the Principal
Now,
∵ If the Amount is 108, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/108
∴ If the Amount is 3564, then the Principal = 100/108 × 3564
= 100 × 3564/108
= 356400/108
= 3300
Thus, Principal = $3300
Thus, the sum borrowed = $3300 Answer
Similar Questions
(1) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8024 to clear the loan, then find the time period of the loan.
(2) Robert had to pay $3472 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 8 years.
(4) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 3 years.
(5) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 7% simple interest?
(6) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.
(7) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 3 years.
(9) In how much time a principal of $3150 will amount to $3465 at a simple interest of 5% per annum?
(10) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 5% simple interest?