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) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(2) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 7 years.
(4) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.
(5) Find the amount to be paid if Susan borrowed a sum of $5650 at 3% simple interest for 7 years.
(6) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $10496 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.
(8) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 3% simple interest?
(9) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.
(10) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $7840 to clear the loan, then find the time period of the loan.