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) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 7 years.
(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 3 years.
(4) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5960 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.
(6) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.
(7) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 3% simple interest?
(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 8 years.
(9) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 3 years.
(10) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.