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 James borrowed a sum of $3000 at 10% simple interest for 4 years.
(2) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 3% simple interest?
(3) If Mary borrowed $3050 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 4% simple interest for 3 years.
(5) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 8 years.
(6) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11340 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.
(8) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7301 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(10) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.