Question:
Paul had to pay $5264 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
Correct Answer
$4700
Solution And Explanation
Solution
Given,
Amount (A) = $5264
Rate of Simple Interest (R) = 4%
Time (T) = 3 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
$5264 = P (1 + 4% × 3)
⇒ $5264 = P (1 + 4/100 × 3)
⇒ $5264 = P (1 + 4 × 3/100)
⇒ $5264 = P (1 + 12/100)
⇒ $5264 = P (100 + 12/100)
⇒ $5264 = P × 112/100
⇒ P × 112/100 = $5264
⇒ P = 5264/112/100
⇒ P = 5264 × 100/112
⇒ P = 5264 × 100/112
⇒ P = 526400/112
⇒ 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 = 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 = 3 years
So, we need to calculate the simple interest for the given time period, which is 3 years
Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year
= 3 × 4 = 12
Thus, simple interest for 3 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 5264, then the Principal = 100/112 × 5264
= 100 × 5264/112
= 526400/112
= 4700
Thus, Principal = $4700
Thus, the sum borrowed = $4700 Answer
Similar Questions
(1) If Linda paid $3618 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.
(4) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 8 years.
(5) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(6) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 6% simple interest?
(7) What amount will be due after 2 years if John borrowed a sum of $3100 at a 4% simple interest?
(8) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 7 years.
(9) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.
(10) How much loan did Melissa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8085 to clear it?