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) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 5% simple interest.
(2) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 7 years.
(4) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.
(5) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(6) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 4 years.
(7) How much loan did Susan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6215 to clear it?
(8) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 4 years.
(10) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 9% simple interest?