Question:
How much loan did Christopher borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7500 to clear it?
Correct Answer
$6000
Solution And Explanation
Solution
Given,
Amount (A) = $7500
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
$7500 = P (1 + 5% × 5)
⇒ $7500 = P (1 + 5/100 × 5)
⇒ $7500 = P (1 + 5 × 5/100)
⇒ $7500 = P (1 + 25/100)
⇒ $7500 = P (100 + 25/100)
⇒ $7500 = P × 125/100
⇒ P × 125/100 = $7500
⇒ P = 7500/125/100
⇒ P = 7500 × 100/125
⇒ P = 7500 × 100/125
⇒ P = 750000/125
⇒ P = $6000
Thus, the sum borrowed (P) = $6000 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 7500, then the Principal = 100/125 × 7500
= 100 × 7500/125
= 750000/125
= 6000
Thus, Principal = $6000
Thus, the sum borrowed = $6000 Answer
Similar Questions
(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 6% simple interest for 7 years.
(2) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 3 years.
(3) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 3% simple interest?
(4) Susan had to pay $4088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10332 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
(7) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 9% simple interest?
(8) If Sarah paid $4620 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) How much loan did Daniel borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7625 to clear it?
(10) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 7% simple interest.