Question:
Andrew had to pay $5232 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
$4800
Solution And Explanation
Solution
Given,
Amount (A) = $5232
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
$5232 = P (1 + 3% × 3)
⇒ $5232 = P (1 + 3/100 × 3)
⇒ $5232 = P (1 + 3 × 3/100)
⇒ $5232 = P (1 + 9/100)
⇒ $5232 = P (100 + 9/100)
⇒ $5232 = P × 109/100
⇒ P × 109/100 = $5232
⇒ P = 5232/109/100
⇒ P = 5232 × 100/109
⇒ P = 5232 × 100/109
⇒ P = 523200/109
⇒ P = $4800
Thus, the sum borrowed (P) = $4800 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 5232, then the Principal = 100/109 × 5232
= 100 × 5232/109
= 523200/109
= 4800
Thus, Principal = $4800
Thus, the sum borrowed = $4800 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 3 years.
(3) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 7% simple interest.
(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 7 years.
(6) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 7 years.
(7) Calculate the amount due if Michael borrowed a sum of $3300 at 8% simple interest for 4 years.
(8) Sarah had to pay $4081 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 7 years.
(10) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 3 years.