Question:
Karen had to pay $4424 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
$3950
Solution And Explanation
Solution
Given,
Amount (A) = $4424
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
$4424 = P (1 + 4% × 3)
⇒ $4424 = P (1 + 4/100 × 3)
⇒ $4424 = P (1 + 4 × 3/100)
⇒ $4424 = P (1 + 12/100)
⇒ $4424 = P (100 + 12/100)
⇒ $4424 = P × 112/100
⇒ P × 112/100 = $4424
⇒ P = 4424/112/100
⇒ P = 4424 × 100/112
⇒ P = 4424 × 100/112
⇒ P = 442400/112
⇒ P = $3950
Thus, the sum borrowed (P) = $3950 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 4424, then the Principal = 100/112 × 4424
= 100 × 4424/112
= 442400/112
= 3950
Thus, Principal = $3950
Thus, the sum borrowed = $3950 Answer
Similar Questions
(1) What amount does John have to pay after 6 years if he takes a loan of $3200 at 10% simple interest?
(2) 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.
(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 8 years.
(4) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.
(5) John had to pay $3488 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 4 years.
(8) How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?
(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 4 years.
(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 7 years.