Question:
How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?
Correct Answer
$7800
Solution And Explanation
Solution
Given,
Amount (A) = $9750
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
$9750 = P (1 + 5% × 5)
⇒ $9750 = P (1 + 5/100 × 5)
⇒ $9750 = P (1 + 5 × 5/100)
⇒ $9750 = P (1 + 25/100)
⇒ $9750 = P (100 + 25/100)
⇒ $9750 = P × 125/100
⇒ P × 125/100 = $9750
⇒ P = 9750/125/100
⇒ P = 9750 × 100/125
⇒ P = 9750 × 100/125
⇒ P = 975000/125
⇒ P = $7800
Thus, the sum borrowed (P) = $7800 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 9750, then the Principal = 100/125 × 9750
= 100 × 9750/125
= 975000/125
= 7800
Thus, Principal = $7800
Thus, the sum borrowed = $7800 Answer
Similar Questions
(1) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 3 years.
(2) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.
(3) Kimberly had to pay $5347.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 3% simple interest?
(5) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 3 years.
(6) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 4% simple interest?
(7) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 2% simple interest?
(8) Calculate the amount due if Michael borrowed a sum of $3300 at 4% simple interest for 3 years.
(9) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.
(10) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.