Question:
How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?
Correct Answer
$6000
Solution And Explanation
Solution
Given,
Amount (A) = $7200
Rate of Simple Interest (R) = 4%
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
$7200 = P (1 + 4% × 5)
⇒ $7200 = P (1 + 4/100 × 5)
⇒ $7200 = P (1 + 4 × 5/100)
⇒ $7200 = P (1 + 20/100)
⇒ $7200 = P (100 + 20/100)
⇒ $7200 = P × 120/100
⇒ P × 120/100 = $7200
⇒ P = 7200/120/100
⇒ P = 7200 × 100/120
⇒ P = 7200 × 100/120
⇒ P = 720000/120
⇒ 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 7200, then the Principal = 100/120 × 7200
= 100 × 7200/120
= 720000/120
= 6000
Thus, Principal = $6000
Thus, the sum borrowed = $6000 Answer
Similar Questions
(1) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 3 years.
(3) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 8% simple interest?
(4) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 5% simple interest?
(6) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 3% simple interest.
(8) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.
(9) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 10% simple interest?
(10) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12308 to clear the loan, then find the time period of the loan.