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) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 8% simple interest?
(2) What amount does David have to pay after 5 years if he takes a loan of $3400 at 2% simple interest?
(3) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.
(4) If Steven paid $5152 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) How much loan did Carol borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8460 to clear it?
(6) If Michael paid $3696 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.
(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) If Joseph borrowed $3700 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(10) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 8 years.