Question:
How much loan did Matthew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6820 to clear it?
Correct Answer
$6200
Solution And Explanation
Solution
Given,
Amount (A) = $6820
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
$6820 = P (1 + 2% × 5)
⇒ $6820 = P (1 + 2/100 × 5)
⇒ $6820 = P (1 + 2 × 5/100)
⇒ $6820 = P (1 + 10/100)
⇒ $6820 = P (100 + 10/100)
⇒ $6820 = P × 110/100
⇒ P × 110/100 = $6820
⇒ P = 6820/110/100
⇒ P = 6820 × 100/110
⇒ P = 6820 × 100/110
⇒ P = 682000/110
⇒ P = $6200
Thus, the sum borrowed (P) = $6200 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 6820, then the Principal = 100/110 × 6820
= 100 × 6820/110
= 682000/110
= 6200
Thus, Principal = $6200
Thus, the sum borrowed = $6200 Answer
Similar Questions
(1) If Donna paid $5626 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6683 to clear the loan, then find the time period of the loan.
(3) What amount does James have to pay after 6 years if he takes a loan of $3000 at 2% simple interest?
(4) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 4% simple interest?
(5) What amount does John have to pay after 5 years if he takes a loan of $3200 at 2% simple interest?
(6) If Joseph paid $4292 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 9% simple interest.
(8) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $9116 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Robert borrowed a sum of $3100 at 3% simple interest for 4 years.
(10) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.