Question:
How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?
Correct Answer
$6750
Solution And Explanation
Solution
Given,
Amount (A) = $7425
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
$7425 = P (1 + 2% × 5)
⇒ $7425 = P (1 + 2/100 × 5)
⇒ $7425 = P (1 + 2 × 5/100)
⇒ $7425 = P (1 + 10/100)
⇒ $7425 = P (100 + 10/100)
⇒ $7425 = P × 110/100
⇒ P × 110/100 = $7425
⇒ P = 7425/110/100
⇒ P = 7425 × 100/110
⇒ P = 7425 × 100/110
⇒ P = 742500/110
⇒ P = $6750
Thus, the sum borrowed (P) = $6750 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 7425, then the Principal = 100/110 × 7425
= 100 × 7425/110
= 742500/110
= 6750
Thus, Principal = $6750
Thus, the sum borrowed = $6750 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(2) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 8% simple interest?
(3) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 4 years.
(4) How much loan did Edward borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8740 to clear it?
(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 7% simple interest for 8 years.
(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 7 years.
(7) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.
(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 3 years.
(9) Karen had to pay $4424 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8195 to clear the loan, then find the time period of the loan.