Question:
Joshua had to pay $5194 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
$4900
Solution And Explanation
Solution
Given,
Amount (A) = $5194
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
$5194 = P (1 + 2% × 3)
⇒ $5194 = P (1 + 2/100 × 3)
⇒ $5194 = P (1 + 2 × 3/100)
⇒ $5194 = P (1 + 6/100)
⇒ $5194 = P (100 + 6/100)
⇒ $5194 = P × 106/100
⇒ P × 106/100 = $5194
⇒ P = 5194/106/100
⇒ P = 5194 × 100/106
⇒ P = 5194 × 100/106
⇒ P = 519400/106
⇒ P = $4900
Thus, the sum borrowed (P) = $4900 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 5194, then the Principal = 100/106 × 5194
= 100 × 5194/106
= 519400/106
= 4900
Thus, Principal = $4900
Thus, the sum borrowed = $4900 Answer
Similar Questions
(1) Michael had to pay $3498 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 4% simple interest?
(3) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.
(4) In how much time a principal of $3150 will amount to $3780 at a simple interest of 5% per annum?
(5) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $12420 to clear the loan, then find the time period of the loan.
(6) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?
(7) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $10260 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.
(9) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(10) How much loan did Ashley borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8187.5 to clear it?