Question:
( 1 of 10 ) If Paul paid $5076 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
$3807
Correct Answer
$4700
Solution And Explanation
Solution
Given,
Amount (A) = $5076
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
$5076 = P (1 + 2% × 4)
⇒ $5076 = P (1 + 2/100 × 4)
⇒ $5076 = P (1 + 2 × 4/100)
⇒ $5076 = P (1 + 8/100)
⇒ $5076 = P (100 + 8/100)
⇒ $5076 = P × 108/100
⇒ P × 108/100 = $5076
⇒ P = 5076/108/100
⇒ P = 5076 × 100/108
⇒ P = 5076 × 100/108
⇒ P = 507600/108
⇒ P = $4700
Thus, the sum borrowed (P) = $4700 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 5076, then the Principal = 100/108 × 5076
= 100 × 5076/108
= 507600/108
= 4700
Thus, Principal = $4700
Thus, the sum borrowed = $4700 Answer
Similar Questions
(1) If James borrowed $3000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(2) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 5% simple interest.
(3) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.
(4) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(5) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(6) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 2% simple interest?
(7) How much loan did Susan borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6215 to clear it?
(8) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 3 years.
(9) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.
(10) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 3 years.