Question:
( 1 of 10 ) If Sarah paid $4312 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
$3234
Correct Answer
$3850
Solution And Explanation
Solution
Given,
Amount (A) = $4312
Rate of Simple Interest (R) = 3%
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
$4312 = P (1 + 3% × 4)
⇒ $4312 = P (1 + 3/100 × 4)
⇒ $4312 = P (1 + 3 × 4/100)
⇒ $4312 = P (1 + 12/100)
⇒ $4312 = P (100 + 12/100)
⇒ $4312 = P × 112/100
⇒ P × 112/100 = $4312
⇒ P = 4312/112/100
⇒ P = 4312 × 100/112
⇒ P = 4312 × 100/112
⇒ P = 431200/112
⇒ 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 12
Thus, simple interest for 4 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 4312, then the Principal = 100/112 × 4312
= 100 × 4312/112
= 431200/112
= 3850
Thus, Principal = $3850
Thus, the sum borrowed = $3850 Answer
Similar Questions
(1) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9020 to clear the loan, then find the time period of the loan.
(2) How much loan did Melissa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8452.5 to clear it?
(3) If Linda borrowed $3350 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.
(5) Joseph had to pay $4033 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 7 years.
(7) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.
(8) 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.
(9) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.
(10) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.