Question:
How much loan did John borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5720 to clear it?
Correct Answer
$5200
Solution And Explanation
Solution
Given,
Amount (A) = $5720
Rate of Simple Interest (R) = 2%
Time (T) = 5 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
$5720 = P (1 + 2% × 5)
⇒ $5720 = P (1 + 2/100 × 5)
⇒ $5720 = P (1 + 2 × 5/100)
⇒ $5720 = P (1 + 10/100)
⇒ $5720 = P (100 + 10/100)
⇒ $5720 = P × 110/100
⇒ P × 110/100 = $5720
⇒ P = 5720/110/100
⇒ P = 5720 × 100/110
⇒ P = 5720 × 100/110
⇒ P = 572000/110
⇒ P = $5200
Thus, the sum borrowed (P) = $5200 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 = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 5720, then the Principal = 100/110 × 5720
= 100 × 5720/110
= 572000/110
= 5200
Thus, Principal = $5200
Thus, the sum borrowed = $5200 Answer
Similar Questions
(1) What amount does William have to pay after 6 years if he takes a loan of $3500 at 3% simple interest?
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 7 years.
(3) If Sarah borrowed $3850 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(4) Margaret had to pay $5002.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $9400 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 4% simple interest?
(7) In how much time a principal of $3150 will amount to $3465 at a simple interest of 5% per annum?
(8) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $10560 to clear the loan, then find the time period of the loan.
(9) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8688 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.