Question:
Mark had to pay $4928 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
$4400
Solution And Explanation
Solution
Given,
Amount (A) = $4928
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
$4928 = P (1 + 4% × 3)
⇒ $4928 = P (1 + 4/100 × 3)
⇒ $4928 = P (1 + 4 × 3/100)
⇒ $4928 = P (1 + 12/100)
⇒ $4928 = P (100 + 12/100)
⇒ $4928 = P × 112/100
⇒ P × 112/100 = $4928
⇒ P = 4928/112/100
⇒ P = 4928 × 100/112
⇒ P = 4928 × 100/112
⇒ P = 492800/112
⇒ 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 = 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 4928, then the Principal = 100/112 × 4928
= 100 × 4928/112
= 492800/112
= 4400
Thus, Principal = $4400
Thus, the sum borrowed = $4400 Answer
Similar Questions
(1) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 4 years.
(2) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.
(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 7 years.
(4) How much loan did Paul borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8040 to clear it?
(5) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 3% per annum?
(6) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.
(7) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(9) Find the amount to be paid if James borrowed a sum of $5000 at 9% simple interest for 8 years.
(10) If Anthony paid $5160 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.