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) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 8 years.
(2) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9540 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 8 years.
(4) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(5) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 4 years.
(6) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(7) What amount does John have to pay after 5 years if he takes a loan of $3200 at 9% simple interest?
(8) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.
(9) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.