Question:
( 2 of 10 ) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?
(A) 212 2/3% या 212.67%
(B) 318 2/3% या 318.67%
(C) 106 2/3% या 106.67%
(D) 53 2/3% या 53.67%
You selected
$5527.5
Correct Answer
$6700
Solution And Explanation
Solution
Given,
Amount (A) = $7370
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
$7370 = P (1 + 2% × 5)
⇒ $7370 = P (1 + 2/100 × 5)
⇒ $7370 = P (1 + 2 × 5/100)
⇒ $7370 = P (1 + 10/100)
⇒ $7370 = P (100 + 10/100)
⇒ $7370 = P × 110/100
⇒ P × 110/100 = $7370
⇒ P = 7370/110/100
⇒ P = 7370 × 100/110
⇒ P = 7370 × 100/110
⇒ P = 737000/110
⇒ P = $6700
Thus, the sum borrowed (P) = $6700 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 7370, then the Principal = 100/110 × 7370
= 100 × 7370/110
= 737000/110
= 6700
Thus, Principal = $6700
Thus, the sum borrowed = $6700 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 4% simple interest?
(3) If Betty paid $4590 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) How much loan did Edward borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8360 to clear it?
(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 3 years.
(6) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 8 years.
(7) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 9% simple interest?
(8) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.
(9) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.
(10) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 6% simple interest?