Question:
Charles had to pay $4368 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
$3900
Solution And Explanation
Solution
Given,
Amount (A) = $4368
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
$4368 = P (1 + 4% × 3)
⇒ $4368 = P (1 + 4/100 × 3)
⇒ $4368 = P (1 + 4 × 3/100)
⇒ $4368 = P (1 + 12/100)
⇒ $4368 = P (100 + 12/100)
⇒ $4368 = P × 112/100
⇒ P × 112/100 = $4368
⇒ P = 4368/112/100
⇒ P = 4368 × 100/112
⇒ P = 4368 × 100/112
⇒ P = 436800/112
⇒ P = $3900
Thus, the sum borrowed (P) = $3900 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 4368, then the Principal = 100/112 × 4368
= 100 × 4368/112
= 436800/112
= 3900
Thus, Principal = $3900
Thus, the sum borrowed = $3900 Answer
Similar Questions
(1) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 3 years.
(2) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7450 to clear the loan, then find the time period of the loan.
(3) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 7 years.
(5) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 7 years.
(6) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 4 years.
(8) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.
(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 7 years.
(10) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.