Question:
Kenneth had to pay $5300 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
$5000
Solution And Explanation
Solution
Given,
Amount (A) = $5300
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
$5300 = P (1 + 2% × 3)
⇒ $5300 = P (1 + 2/100 × 3)
⇒ $5300 = P (1 + 2 × 3/100)
⇒ $5300 = P (1 + 6/100)
⇒ $5300 = P (100 + 6/100)
⇒ $5300 = P × 106/100
⇒ P × 106/100 = $5300
⇒ P = 5300/106/100
⇒ P = 5300 × 100/106
⇒ P = 5300 × 100/106
⇒ P = 530000/106
⇒ P = $5000
Thus, the sum borrowed (P) = $5000 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 5300, then the Principal = 100/106 × 5300
= 100 × 5300/106
= 530000/106
= 5000
Thus, Principal = $5000
Thus, the sum borrowed = $5000 Answer
Similar Questions
(1) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 8 years.
(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 8 years.
(3) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.
(4) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 4% simple interest?
(5) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.
(6) How much loan did Joshua borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7590 to clear it?
(7) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 10% simple interest?
(8) Anthony had to pay $4945 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) What amount will be due after 2 years if John borrowed a sum of $3100 at a 5% simple interest?
(10) Susan had to pay $4088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.