Question:
How much loan did James borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5750 to clear it?
Correct Answer
$5000
Solution And Explanation
Solution
Given,
Amount (A) = $5750
Rate of Simple Interest (R) = 3%
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
$5750 = P (1 + 3% × 5)
⇒ $5750 = P (1 + 3/100 × 5)
⇒ $5750 = P (1 + 3 × 5/100)
⇒ $5750 = P (1 + 15/100)
⇒ $5750 = P (100 + 15/100)
⇒ $5750 = P × 115/100
⇒ P × 115/100 = $5750
⇒ P = 5750/115/100
⇒ P = 5750 × 100/115
⇒ P = 5750 × 100/115
⇒ P = 575000/115
⇒ P = $5000
Thus, the sum borrowed (P) = $5000 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 5750, then the Principal = 100/115 × 5750
= 100 × 5750/115
= 575000/115
= 5000
Thus, Principal = $5000
Thus, the sum borrowed = $5000 Answer
Similar Questions
(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.
(2) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9050 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Linda borrowed a sum of $3350 at 10% simple interest for 4 years.
(4) If Robert borrowed $3100 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(5) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.
(6) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 10% simple interest?
(7) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 7 years.
(8) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.
(9) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 3% simple interest?
(10) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.