Question:
( 1 of 10 ) If Robert paid $3596 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
$2697
Correct Answer
$3100
Solution And Explanation
Solution
Given,
Amount (A) = $3596
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
$3596 = P (1 + 4% × 4)
⇒ $3596 = P (1 + 4/100 × 4)
⇒ $3596 = P (1 + 4 × 4/100)
⇒ $3596 = P (1 + 16/100)
⇒ $3596 = P (100 + 16/100)
⇒ $3596 = P × 116/100
⇒ P × 116/100 = $3596
⇒ P = 3596/116/100
⇒ P = 3596 × 100/116
⇒ P = 3596 × 100/116
⇒ P = 359600/116
⇒ P = $3100
Thus, the sum borrowed (P) = $3100 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 3596, then the Principal = 100/116 × 3596
= 100 × 3596/116
= 359600/116
= 3100
Thus, Principal = $3100
Thus, the sum borrowed = $3100 Answer
Similar Questions
(1) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.
(2) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 7% simple interest?
(3) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 4 years.
(4) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.
(5) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12800 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 8 years.
(7) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 3 years.
(8) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?
(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 8 years.
(10) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $7888 to clear the loan, then find the time period of the loan.