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) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.
(2) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.
(3) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 4% simple interest.
(5) In how much time a principal of $3200 will amount to $3456 at a simple interest of 4% per annum?
(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 3 years.
(7) In how much time a principal of $3050 will amount to $3172 at a simple interest of 2% per annum?
(8) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 3% simple interest?
(9) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(10) If Jennifer paid $3640 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.