Question:
( 1 of 10 ) If Sarah paid $4466 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
$3349.5
Correct Answer
$3850
Solution And Explanation
Solution
Given,
Amount (A) = $4466
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
$4466 = P (1 + 4% × 4)
⇒ $4466 = P (1 + 4/100 × 4)
⇒ $4466 = P (1 + 4 × 4/100)
⇒ $4466 = P (1 + 16/100)
⇒ $4466 = P (100 + 16/100)
⇒ $4466 = P × 116/100
⇒ P × 116/100 = $4466
⇒ P = 4466/116/100
⇒ P = 4466 × 100/116
⇒ P = 4466 × 100/116
⇒ P = 446600/116
⇒ P = $3850
Thus, the sum borrowed (P) = $3850 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 4466, then the Principal = 100/116 × 4466
= 100 × 4466/116
= 446600/116
= 3850
Thus, Principal = $3850
Thus, the sum borrowed = $3850 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 7% simple interest.
(2) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 3 years.
(3) How much loan did Linda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6420 to clear it?
(4) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
(5) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 10% simple interest?
(6) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(7) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $11400 to clear the loan, then find the time period of the loan.
(8) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(9) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $9200 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 3 years.