Question:
( 1 of 10 ) If Jessica paid $4050 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
$3037.5
Correct Answer
$3750
Solution And Explanation
Solution
Given,
Amount (A) = $4050
Rate of Simple Interest (R) = 2%
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
$4050 = P (1 + 2% × 4)
⇒ $4050 = P (1 + 2/100 × 4)
⇒ $4050 = P (1 + 2 × 4/100)
⇒ $4050 = P (1 + 8/100)
⇒ $4050 = P (100 + 8/100)
⇒ $4050 = P × 108/100
⇒ P × 108/100 = $4050
⇒ P = 4050/108/100
⇒ P = 4050 × 100/108
⇒ P = 4050 × 100/108
⇒ P = 405000/108
⇒ P = $3750
Thus, the sum borrowed (P) = $3750 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 = 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 × 2 = 8
Thus, simple interest for 4 years = 8
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 8 = 108
Calculation of the Principal
Now,
∵ If the Amount is 108, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/108
∴ If the Amount is 4050, then the Principal = 100/108 × 4050
= 100 × 4050/108
= 405000/108
= 3750
Thus, Principal = $3750
Thus, the sum borrowed = $3750 Answer
Similar Questions
(1) How much loan did Margaret borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7937.5 to clear it?
(2) Kenneth had to pay $5450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 3 years.
(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 8 years.
(5) Betty had to pay $4505 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.
(7) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 8 years.
(9) Michael had to pay $3597 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 7 years.