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 Charles borrowed a sum of $3450 at a 7% simple interest?
(2) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8432 to clear the loan, then find the time period of the loan.
(3) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(4) Kimberly had to pay $4929 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 6% simple interest for 4 years.
(6) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
(7) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(8) If Lisa paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7599 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 8 years.