Question:
Barbara had to pay $3976 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
$3550
Solution And Explanation
Solution
Given,
Amount (A) = $3976
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
$3976 = P (1 + 4% × 3)
⇒ $3976 = P (1 + 4/100 × 3)
⇒ $3976 = P (1 + 4 × 3/100)
⇒ $3976 = P (1 + 12/100)
⇒ $3976 = P (100 + 12/100)
⇒ $3976 = P × 112/100
⇒ P × 112/100 = $3976
⇒ P = 3976/112/100
⇒ P = 3976 × 100/112
⇒ P = 3976 × 100/112
⇒ P = 397600/112
⇒ P = $3550
Thus, the sum borrowed (P) = $3550 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 3976, then the Principal = 100/112 × 3976
= 100 × 3976/112
= 397600/112
= 3550
Thus, Principal = $3550
Thus, the sum borrowed = $3550 Answer
Similar Questions
(1) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 3 years.
(3) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 2% simple interest?
(4) 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.
(5) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 3 years.
(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 3 years.
(7) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(8) If Betty paid $4760 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 4 years.
(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 8% simple interest for 4 years.