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) If Richard paid $3888 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(3) Jessica had to pay $4087.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 3% simple interest.
(5) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 3 years.
(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 7 years.
(7) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.
(8) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.
(9) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 4% simple interest?
(10) What amount does James have to pay after 6 years if he takes a loan of $3000 at 2% simple interest?