Question:
( 1 of 10 ) How much loan did David borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5940 to clear it?
(A) 4 47/50 Or, 247/50
(B) 8 47/50 Or, 447/50
(C) 4 141/50 Or, 341/50
(D) 4 94/50 Or, 294/50
You selected
$4455
Correct Answer
$5400
Solution And Explanation
Solution
Given,
Amount (A) = $5940
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
$5940 = P (1 + 2% × 5)
⇒ $5940 = P (1 + 2/100 × 5)
⇒ $5940 = P (1 + 2 × 5/100)
⇒ $5940 = P (1 + 10/100)
⇒ $5940 = P (100 + 10/100)
⇒ $5940 = P × 110/100
⇒ P × 110/100 = $5940
⇒ P = 5940/110/100
⇒ P = 5940 × 100/110
⇒ P = 5940 × 100/110
⇒ P = 594000/110
⇒ P = $5400
Thus, the sum borrowed (P) = $5400 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 5940, then the Principal = 100/110 × 5940
= 100 × 5940/110
= 594000/110
= 5400
Thus, Principal = $5400
Thus, the sum borrowed = $5400 Answer
Similar Questions
(1) If Andrew paid $5568 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) In how much time a principal of $3000 will amount to $3300 at a simple interest of 2% per annum?
(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 3 years.
(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 7 years.
(5) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.
(6) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 6% simple interest?
(8) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?
(9) In how much time a principal of $3100 will amount to $3224 at a simple interest of 2% per annum?
(10) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 7% simple interest?