Question:
How much loan did David borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5940 to clear it?
Correct Answer
$5400
Solution And Explanation
Solution
Given,
Amount (A) = $5940
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
$5940 = P (1 + 2% × 5)
⇒ $5940 = P (1 + 2/100 × 5)
⇒ $5940 = P (1 + 2 × 5/100)
⇒ $5940 = P (1 + 10/100)
⇒ $5940 = P (100 + 10/100)
⇒ $5940 = P × 110/100
⇒ P × 110/100 = $5940
⇒ P = 5940/110/100
⇒ P = 5940 × 100/110
⇒ P = 5940 × 100/110
⇒ P = 594000/110
⇒ P = $5400
Thus, the sum borrowed (P) = $5400 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 5940, then the Principal = 100/110 × 5940
= 100 × 5940/110
= 594000/110
= 5400
Thus, Principal = $5400
Thus, the sum borrowed = $5400 Answer
Similar Questions
(1) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 4 years.
(3) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 8% simple interest?
(4) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?
(5) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.
(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 8 years.
(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 8 years.
(8) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 8% simple interest?
(9) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.
(10) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $11020 to clear the loan, then find the time period of the loan.