Question:
If Karen paid $4266 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$3950
Solution And Explanation
Solution
Given,
Amount (A) = $4266
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
$4266 = P (1 + 2% × 4)
⇒ $4266 = P (1 + 2/100 × 4)
⇒ $4266 = P (1 + 2 × 4/100)
⇒ $4266 = P (1 + 8/100)
⇒ $4266 = P (100 + 8/100)
⇒ $4266 = P × 108/100
⇒ P × 108/100 = $4266
⇒ P = 4266/108/100
⇒ P = 4266 × 100/108
⇒ P = 4266 × 100/108
⇒ P = 426600/108
⇒ P = $3950
Thus, the sum borrowed (P) = $3950 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 4266, then the Principal = 100/108 × 4266
= 100 × 4266/108
= 426600/108
= 3950
Thus, Principal = $3950
Thus, the sum borrowed = $3950 Answer
Similar Questions
(1) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(2) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.
(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 8 years.
(5) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8670 to clear the loan, then find the time period of the loan.
(6) What amount does James have to pay after 6 years if he takes a loan of $3000 at 8% simple interest?
(7) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $7810 to clear the loan, then find the time period of the loan.
(8) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11800 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Susan borrowed a sum of $3650 at 4% simple interest for 3 years.
(10) How much loan did Margaret borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7937.5 to clear it?