Question:
How much loan did George borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8395 to clear it?
Correct Answer
$7300
Solution And Explanation
Solution
Given,
Amount (A) = $8395
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
$8395 = P (1 + 3% × 5)
⇒ $8395 = P (1 + 3/100 × 5)
⇒ $8395 = P (1 + 3 × 5/100)
⇒ $8395 = P (1 + 15/100)
⇒ $8395 = P (100 + 15/100)
⇒ $8395 = P × 115/100
⇒ P × 115/100 = $8395
⇒ P = 8395/115/100
⇒ P = 8395 × 100/115
⇒ P = 8395 × 100/115
⇒ P = 839500/115
⇒ P = $7300
Thus, the sum borrowed (P) = $7300 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 8395, then the Principal = 100/115 × 8395
= 100 × 8395/115
= 839500/115
= 7300
Thus, Principal = $7300
Thus, the sum borrowed = $7300 Answer
Similar Questions
(1) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 7% simple interest?
(2) If Sarah paid $4312 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) How much loan did Karen borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6842.5 to clear it?
(4) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 4% simple interest?
(6) What amount does David have to pay after 5 years if he takes a loan of $3400 at 10% simple interest?
(7) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 7 years.
(9) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 8 years.
(10) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 6% simple interest?