Question:
Lisa had to pay $4293 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
Correct Answer
$4050
Solution And Explanation
Solution
Given,
Amount (A) = $4293
Rate of Simple Interest (R) = 2%
Time (T) = 3 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
$4293 = P (1 + 2% × 3)
⇒ $4293 = P (1 + 2/100 × 3)
⇒ $4293 = P (1 + 2 × 3/100)
⇒ $4293 = P (1 + 6/100)
⇒ $4293 = P (100 + 6/100)
⇒ $4293 = P × 106/100
⇒ P × 106/100 = $4293
⇒ P = 4293/106/100
⇒ P = 4293 × 100/106
⇒ P = 4293 × 100/106
⇒ P = 429300/106
⇒ P = $4050
Thus, the sum borrowed (P) = $4050 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 = 3 years
So, we need to calculate the simple interest for the given time period, which is 3 years
Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year
= 3 × 2 = 6
Thus, simple interest for 3 years = 6
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 6 = 106
Calculation of the Principal
Now,
∵ If the Amount is 106, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/106
∴ If the Amount is 4293, then the Principal = 100/106 × 4293
= 100 × 4293/106
= 429300/106
= 4050
Thus, Principal = $4050
Thus, the sum borrowed = $4050 Answer
Similar Questions
(1) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 7 years.
(2) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 8% simple interest?
(3) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $8736 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 10% simple interest?
(5) Linda had to pay $3651.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 3 years.
(7) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9900 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 3 years.
(9) How much loan did Emily borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7762.5 to clear it?
(10) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 5% simple interest.