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) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.
(3) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 7% simple interest?
(4) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 8 years.
(5) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 8 years.
(7) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 3% simple interest?
(8) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 4 years.
(10) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6854 to clear the loan, then find the time period of the loan.