Question:
( 3 of 10 ) If John paid $3712 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(A) 11 19/46 days or 11.413 days
(B) 22 19/46 days or 22.413 days
(C) 46 days
(D) 23 days
You selected
$2784
Correct Answer
$3200
Solution And Explanation
Solution
Given,
Amount (A) = $3712
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
$3712 = P (1 + 4% × 4)
⇒ $3712 = P (1 + 4/100 × 4)
⇒ $3712 = P (1 + 4 × 4/100)
⇒ $3712 = P (1 + 16/100)
⇒ $3712 = P (100 + 16/100)
⇒ $3712 = P × 116/100
⇒ P × 116/100 = $3712
⇒ P = 3712/116/100
⇒ P = 3712 × 100/116
⇒ P = 3712 × 100/116
⇒ P = 371200/116
⇒ P = $3200
Thus, the sum borrowed (P) = $3200 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 3712, then the Principal = 100/116 × 3712
= 100 × 3712/116
= 371200/116
= 3200
Thus, Principal = $3200
Thus, the sum borrowed = $3200 Answer
Similar Questions
(1) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.
(2) If John paid $3840 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 3% simple interest?
(4) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 7 years.
(5) If Michelle paid $5742 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(6) If Ashley paid $5278 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 7 years.
(8) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.
(10) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.