Question:
How much loan did Ronald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9375 to clear it?
Correct Answer
$7500
Solution And Explanation
Solution
Given,
Amount (A) = $9375
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
$9375 = P (1 + 5% × 5)
⇒ $9375 = P (1 + 5/100 × 5)
⇒ $9375 = P (1 + 5 × 5/100)
⇒ $9375 = P (1 + 25/100)
⇒ $9375 = P (100 + 25/100)
⇒ $9375 = P × 125/100
⇒ P × 125/100 = $9375
⇒ P = 9375/125/100
⇒ P = 9375 × 100/125
⇒ P = 9375 × 100/125
⇒ P = 937500/125
⇒ P = $7500
Thus, the sum borrowed (P) = $7500 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 9375, then the Principal = 100/125 × 9375
= 100 × 9375/125
= 937500/125
= 7500
Thus, Principal = $7500
Thus, the sum borrowed = $7500 Answer
Similar Questions
(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 4 years.
(2) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 7% simple interest?
(3) How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?
(4) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.
(6) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.
(7) If Ashley paid $5096 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?
(9) Calculate the amount due if Michael borrowed a sum of $3300 at 2% simple interest for 3 years.
(10) Sarah had to pay $4312 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.