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 after 9 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.
(2) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 2% simple interest?
(3) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7790 to clear the loan, then find the time period of the loan.
(4) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 7% simple interest?
(5) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 9% simple interest?
(6) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 9% simple interest?
(7) Joseph had to pay $4255 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) In how much time a principal of $3100 will amount to $3348 at a simple interest of 2% per annum?
(9) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 4 years.
(10) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.