Question:
How much loan did Dorothy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7975 to clear it?
Correct Answer
$7250
Solution And Explanation
Solution
Given,
Amount (A) = $7975
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
$7975 = P (1 + 2% × 5)
⇒ $7975 = P (1 + 2/100 × 5)
⇒ $7975 = P (1 + 2 × 5/100)
⇒ $7975 = P (1 + 10/100)
⇒ $7975 = P (100 + 10/100)
⇒ $7975 = P × 110/100
⇒ P × 110/100 = $7975
⇒ P = 7975/110/100
⇒ P = 7975 × 100/110
⇒ P = 7975 × 100/110
⇒ P = 797500/110
⇒ P = $7250
Thus, the sum borrowed (P) = $7250 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 7975, then the Principal = 100/110 × 7975
= 100 × 7975/110
= 797500/110
= 7250
Thus, Principal = $7250
Thus, the sum borrowed = $7250 Answer
Similar Questions
(1) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 3 years.
(2) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.
(3) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.
(4) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 8 years.
(6) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.
(7) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 3 years.
(8) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 3 years.
(10) Lisa had to pay $4414.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.