Question:
How much loan did Betty borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6875 to clear it?
Correct Answer
$6250
Solution And Explanation
Solution
Given,
Amount (A) = $6875
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
$6875 = P (1 + 2% × 5)
⇒ $6875 = P (1 + 2/100 × 5)
⇒ $6875 = P (1 + 2 × 5/100)
⇒ $6875 = P (1 + 10/100)
⇒ $6875 = P (100 + 10/100)
⇒ $6875 = P × 110/100
⇒ P × 110/100 = $6875
⇒ P = 6875/110/100
⇒ P = 6875 × 100/110
⇒ P = 6875 × 100/110
⇒ P = 687500/110
⇒ P = $6250
Thus, the sum borrowed (P) = $6250 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 6875, then the Principal = 100/110 × 6875
= 100 × 6875/110
= 687500/110
= 6250
Thus, Principal = $6250
Thus, the sum borrowed = $6250 Answer
Similar Questions
(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 4 years.
(2) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(3) If Michael borrowed $3300 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(4) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.
(5) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 9% simple interest.
(7) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?
(9) Calculate the amount due if John borrowed a sum of $3200 at 9% simple interest for 3 years.
(10) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.