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) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 6% simple interest?
(2) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 3 years.
(3) 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.
(4) What amount does William have to pay after 6 years if he takes a loan of $3500 at 6% simple interest?
(5) How much loan did Michelle borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7645 to clear it?
(6) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.
(7) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 8% simple interest?
(8) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 4 years.
(10) Susan had to pay $4197.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.