Question:
How much loan did John borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5980 to clear it?
Correct Answer
$5200
Solution And Explanation
Solution
Given,
Amount (A) = $5980
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
$5980 = P (1 + 3% × 5)
⇒ $5980 = P (1 + 3/100 × 5)
⇒ $5980 = P (1 + 3 × 5/100)
⇒ $5980 = P (1 + 15/100)
⇒ $5980 = P (100 + 15/100)
⇒ $5980 = P × 115/100
⇒ P × 115/100 = $5980
⇒ P = 5980/115/100
⇒ P = 5980 × 100/115
⇒ P = 5980 × 100/115
⇒ P = 598000/115
⇒ P = $5200
Thus, the sum borrowed (P) = $5200 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 5980, then the Principal = 100/115 × 5980
= 100 × 5980/115
= 598000/115
= 5200
Thus, Principal = $5200
Thus, the sum borrowed = $5200 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.
(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 7 years.
(3) How much loan did Betty borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7812.5 to clear it?
(4) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 2% simple interest?
(5) In how much time a principal of $3200 will amount to $3488 at a simple interest of 3% per annum?
(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 8 years.
(7) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.
(9) If Linda paid $3618 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 7 years.