Question:
Christopher had to pay $4480 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
$4000
Solution And Explanation
Solution
Given,
Amount (A) = $4480
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
$4480 = P (1 + 4% × 3)
⇒ $4480 = P (1 + 4/100 × 3)
⇒ $4480 = P (1 + 4 × 3/100)
⇒ $4480 = P (1 + 12/100)
⇒ $4480 = P (100 + 12/100)
⇒ $4480 = P × 112/100
⇒ P × 112/100 = $4480
⇒ P = 4480/112/100
⇒ P = 4480 × 100/112
⇒ P = 4480 × 100/112
⇒ P = 448000/112
⇒ P = $4000
Thus, the sum borrowed (P) = $4000 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 4480, then the Principal = 100/112 × 4480
= 100 × 4480/112
= 448000/112
= 4000
Thus, Principal = $4000
Thus, the sum borrowed = $4000 Answer
Similar Questions
(1) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 10% simple interest?
(3) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 7 years.
(4) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $9593 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 7 years.
(6) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.
(7) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 3 years.
(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 8 years.
(10) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.