Question:
( 1 of 10 ) If Joshua paid $5684 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
$4263
Correct Answer
$4900
Solution And Explanation
Solution
Given,
Amount (A) = $5684
Rate of Simple Interest (R) = 4%
Time (T) = 4 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
$5684 = P (1 + 4% × 4)
⇒ $5684 = P (1 + 4/100 × 4)
⇒ $5684 = P (1 + 4 × 4/100)
⇒ $5684 = P (1 + 16/100)
⇒ $5684 = P (100 + 16/100)
⇒ $5684 = P × 116/100
⇒ P × 116/100 = $5684
⇒ P = 5684/116/100
⇒ P = 5684 × 100/116
⇒ P = 5684 × 100/116
⇒ P = 568400/116
⇒ P = $4900
Thus, the sum borrowed (P) = $4900 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
Calculation of the Amount
Since, in the question, time = 4 years
So, we need to calculate the simple interest for the given time period, which is 4 years
Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year
= 4 × 4 = 16
Thus, simple interest for 4 years = 16
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 16 = 116
Calculation of the Principal
Now,
∵ If the Amount is 116, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/116
∴ If the Amount is 5684, then the Principal = 100/116 × 5684
= 100 × 5684/116
= 568400/116
= 4900
Thus, Principal = $4900
Thus, the sum borrowed = $4900 Answer
Similar Questions
(1) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 4 years.
(2) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.
(3) How much loan did Deborah borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8195 to clear it?
(4) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.
(5) 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?
(6) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 5% simple interest?
(7) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.
(8) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 7 years.
(9) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11403 to clear the loan, then find the time period of the loan.
(10) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 3% simple interest?