Question:
Jennifer had to pay $3640 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
$3250
Solution And Explanation
Solution
Given,
Amount (A) = $3640
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
$3640 = P (1 + 4% × 3)
⇒ $3640 = P (1 + 4/100 × 3)
⇒ $3640 = P (1 + 4 × 3/100)
⇒ $3640 = P (1 + 12/100)
⇒ $3640 = P (100 + 12/100)
⇒ $3640 = P × 112/100
⇒ P × 112/100 = $3640
⇒ P = 3640/112/100
⇒ P = 3640 × 100/112
⇒ P = 3640 × 100/112
⇒ P = 364000/112
⇒ P = $3250
Thus, the sum borrowed (P) = $3250 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 3640, then the Principal = 100/112 × 3640
= 100 × 3640/112
= 364000/112
= 3250
Thus, Principal = $3250
Thus, the sum borrowed = $3250 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.
(2) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 3 years.
(3) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.
(4) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $8460 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 7 years.
(6) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 4 years.
(7) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 2% simple interest?
(8) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.
(10) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 8 years.