Question:
How much loan did Christopher borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6600 to clear it?
Correct Answer
$6000
Solution And Explanation
Solution
Given,
Amount (A) = $6600
Rate of Simple Interest (R) = 2%
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
$6600 = P (1 + 2% × 5)
⇒ $6600 = P (1 + 2/100 × 5)
⇒ $6600 = P (1 + 2 × 5/100)
⇒ $6600 = P (1 + 10/100)
⇒ $6600 = P (100 + 10/100)
⇒ $6600 = P × 110/100
⇒ P × 110/100 = $6600
⇒ P = 6600/110/100
⇒ P = 6600 × 100/110
⇒ P = 6600 × 100/110
⇒ P = 660000/110
⇒ 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 6600, then the Principal = 100/110 × 6600
= 100 × 6600/110
= 660000/110
= 6000
Thus, Principal = $6000
Thus, the sum borrowed = $6000 Answer
Similar Questions
(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 8 years.
(2) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.
(3) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 10% simple interest.
(5) In how much time a principal of $3200 will amount to $3520 at a simple interest of 2% per annum?
(6) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.
(7) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 10% simple interest?
(9) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 4 years.
(10) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.