Question:
( 1 of 10 ) How much loan did Sarah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6435 to clear it?
(A) 618 1/11% या 618.09%
(B) 927 1/11% या 927.09%
(C) 154 1/11% या 154.09%
(D) 309 1/11% या 309.09%
You selected
$4826.25
Correct Answer
$5850
Solution And Explanation
Solution
Given,
Amount (A) = $6435
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
$6435 = P (1 + 2% × 5)
⇒ $6435 = P (1 + 2/100 × 5)
⇒ $6435 = P (1 + 2 × 5/100)
⇒ $6435 = P (1 + 10/100)
⇒ $6435 = P (100 + 10/100)
⇒ $6435 = P × 110/100
⇒ P × 110/100 = $6435
⇒ P = 6435/110/100
⇒ P = 6435 × 100/110
⇒ P = 6435 × 100/110
⇒ P = 643500/110
⇒ P = $5850
Thus, the sum borrowed (P) = $5850 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 6435, then the Principal = 100/110 × 6435
= 100 × 6435/110
= 643500/110
= 5850
Thus, Principal = $5850
Thus, the sum borrowed = $5850 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 9% simple interest?
(3) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.
(4) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 8 years.
(5) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 9% simple interest?
(6) How much loan did Paul borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7705 to clear it?
(7) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 3 years.
(8) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 7 years.
(10) How much loan did Jacob borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $10000 to clear it?