Question:
How much loan did Matthew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7440 to clear it?
Correct Answer
$6200
Solution And Explanation
Solution
Given,
Amount (A) = $7440
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
$7440 = P (1 + 4% × 5)
⇒ $7440 = P (1 + 4/100 × 5)
⇒ $7440 = P (1 + 4 × 5/100)
⇒ $7440 = P (1 + 20/100)
⇒ $7440 = P (100 + 20/100)
⇒ $7440 = P × 120/100
⇒ P × 120/100 = $7440
⇒ P = 7440/120/100
⇒ P = 7440 × 100/120
⇒ P = 7440 × 100/120
⇒ P = 744000/120
⇒ P = $6200
Thus, the sum borrowed (P) = $6200 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 7440, then the Principal = 100/120 × 7440
= 100 × 7440/120
= 744000/120
= 6200
Thus, Principal = $6200
Thus, the sum borrowed = $6200 Answer
Similar Questions
(1) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12127 to clear the loan, then find the time period of the loan.
(2) What amount does John have to pay after 5 years if he takes a loan of $3200 at 2% simple interest?
(3) If Richard borrowed $3600 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(4) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 9% simple interest.
(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 4 years.
(6) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.
(7) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 8 years.
(9) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 3% simple interest?
(10) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.