Question:
Andrew had to pay $5088 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
$4800
Solution And Explanation
Solution
Given,
Amount (A) = $5088
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
$5088 = P (1 + 2% × 3)
⇒ $5088 = P (1 + 2/100 × 3)
⇒ $5088 = P (1 + 2 × 3/100)
⇒ $5088 = P (1 + 6/100)
⇒ $5088 = P (100 + 6/100)
⇒ $5088 = P × 106/100
⇒ P × 106/100 = $5088
⇒ P = 5088/106/100
⇒ P = 5088 × 100/106
⇒ P = 5088 × 100/106
⇒ P = 508800/106
⇒ P = $4800
Thus, the sum borrowed (P) = $4800 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 5088, then the Principal = 100/106 × 5088
= 100 × 5088/106
= 508800/106
= 4800
Thus, Principal = $4800
Thus, the sum borrowed = $4800 Answer
Similar Questions
(1) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 8 years.
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 8 years.
(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 8 years.
(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 8 years.
(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 3% simple interest for 8 years.
(6) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?
(7) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.
(8) How much loan did Thomas borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6670 to clear it?
(9) If Margaret paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 6% simple interest?