Question:
Matthew had to pay $4578 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
$4200
Solution And Explanation
Solution
Given,
Amount (A) = $4578
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
$4578 = P (1 + 3% × 3)
⇒ $4578 = P (1 + 3/100 × 3)
⇒ $4578 = P (1 + 3 × 3/100)
⇒ $4578 = P (1 + 9/100)
⇒ $4578 = P (100 + 9/100)
⇒ $4578 = P × 109/100
⇒ P × 109/100 = $4578
⇒ P = 4578/109/100
⇒ P = 4578 × 100/109
⇒ P = 4578 × 100/109
⇒ P = 457800/109
⇒ P = $4200
Thus, the sum borrowed (P) = $4200 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 4578, then the Principal = 100/109 × 4578
= 100 × 4578/109
= 457800/109
= 4200
Thus, Principal = $4200
Thus, the sum borrowed = $4200 Answer
Similar Questions
(1) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 4 years.
(2) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.
(3) Margaret had to pay $4741.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) What amount will be due after 2 years if David borrowed a sum of $3200 at a 5% simple interest?
(5) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 8 years.
(6) If Mary borrowed $3050 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 8 years.
(8) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 7 years.
(9) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 4 years.
(10) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.