Question:
If Mark paid $5104 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$4400
Solution And Explanation
Solution
Given,
Amount (A) = $5104
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
$5104 = P (1 + 4% × 4)
⇒ $5104 = P (1 + 4/100 × 4)
⇒ $5104 = P (1 + 4 × 4/100)
⇒ $5104 = P (1 + 16/100)
⇒ $5104 = P (100 + 16/100)
⇒ $5104 = P × 116/100
⇒ P × 116/100 = $5104
⇒ P = 5104/116/100
⇒ P = 5104 × 100/116
⇒ P = 5104 × 100/116
⇒ P = 510400/116
⇒ P = $4400
Thus, the sum borrowed (P) = $4400 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 5104, then the Principal = 100/116 × 5104
= 100 × 5104/116
= 510400/116
= 4400
Thus, Principal = $4400
Thus, the sum borrowed = $4400 Answer
Similar Questions
(1) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 7% simple interest?
(2) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 4 years.
(3) Lisa had to pay $4536 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.
(5) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9840 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 8 years.
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 7 years.
(8) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 4 years.
(9) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 6% simple interest?
(10) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 4 years.