Question:
Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
Correct Answer
$3550
Solution And Explanation
Solution
Given,
Amount (A) = $3869.5
Rate of Simple Interest (R) = 3%
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
$3869.5 = P (1 + 3% × 3)
⇒ $3869.5 = P (1 + 3/100 × 3)
⇒ $3869.5 = P (1 + 3 × 3/100)
⇒ $3869.5 = P (1 + 9/100)
⇒ $3869.5 = P (100 + 9/100)
⇒ $3869.5 = P × 109/100
⇒ P × 109/100 = $3869.5
⇒ P = 3869.5/109/100
⇒ P = 3869.5 × 100/109
⇒ P = 3869.5 × 100/109
⇒ P = 386950/109
⇒ 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 9
Thus, simple interest for 3 years = 9
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 9 = 109
Calculation of the Principal
Now,
∵ If the Amount is 109, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/109
∴ If the Amount is 3869.5, then the Principal = 100/109 × 3869.5
= 100 × 3869.5/109
= 386950/109
= 3550
Thus, Principal = $3550
Thus, the sum borrowed = $3550 Answer
Similar Questions
(1) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 8 years.
(3) If Sarah borrowed $3850 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(4) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 4 years.
(5) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 9% simple interest.
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 7 years.
(8) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 8 years.
(10) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 10% simple interest?