Question:
How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?
Correct Answer
$5200
Solution And Explanation
Solution
Given,
Amount (A) = $6240
Rate of Simple Interest (R) = 4%
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
$6240 = P (1 + 4% × 5)
⇒ $6240 = P (1 + 4/100 × 5)
⇒ $6240 = P (1 + 4 × 5/100)
⇒ $6240 = P (1 + 20/100)
⇒ $6240 = P (100 + 20/100)
⇒ $6240 = P × 120/100
⇒ P × 120/100 = $6240
⇒ P = 6240/120/100
⇒ P = 6240 × 100/120
⇒ P = 6240 × 100/120
⇒ P = 624000/120
⇒ 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 6240, then the Principal = 100/120 × 6240
= 100 × 6240/120
= 624000/120
= 5200
Thus, Principal = $5200
Thus, the sum borrowed = $5200 Answer
Similar Questions
(1) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $11730 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 8% simple interest?
(3) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 9% simple interest.
(4) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 7 years.
(5) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.
(6) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 2% simple interest?
(7) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 8% simple interest?
(8) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 8% simple interest.
(9) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 8% simple interest?
(10) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.