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 if Mary borrowed a sum of $3050 at 5% simple interest for 4 years.
(2) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 7% simple interest?
(3) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.
(4) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(5) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 7% simple interest.
(7) In how much time a principal of $3050 will amount to $3416 at a simple interest of 3% per annum?
(8) 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.
(9) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 8 years.
(10) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.