Question:
How much loan did George borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9125 to clear it?
Correct Answer
$7300
Solution And Explanation
Solution
Given,
Amount (A) = $9125
Rate of Simple Interest (R) = 5%
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
$9125 = P (1 + 5% × 5)
⇒ $9125 = P (1 + 5/100 × 5)
⇒ $9125 = P (1 + 5 × 5/100)
⇒ $9125 = P (1 + 25/100)
⇒ $9125 = P (100 + 25/100)
⇒ $9125 = P × 125/100
⇒ P × 125/100 = $9125
⇒ P = 9125/125/100
⇒ P = 9125 × 100/125
⇒ P = 9125 × 100/125
⇒ P = 912500/125
⇒ 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 9125, then the Principal = 100/125 × 9125
= 100 × 9125/125
= 912500/125
= 7300
Thus, Principal = $7300
Thus, the sum borrowed = $7300 Answer
Similar Questions
(1) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8960 to clear the loan, then find the time period of the loan.
(2) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $9200 to clear the loan, then find the time period of the loan.
(3) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.
(4) If Mark paid $4928 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7040 to clear the loan, then find the time period of the loan.
(6) Paul had to pay $4982 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 3 years.
(8) How much loan did John borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6500 to clear it?
(9) What amount does William have to pay after 6 years if he takes a loan of $3500 at 7% simple interest?
(10) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 3% simple interest?