Question:
Michelle had to pay $5395.5 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
$4950
Solution And Explanation
Solution
Given,
Amount (A) = $5395.5
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
$5395.5 = P (1 + 3% × 3)
⇒ $5395.5 = P (1 + 3/100 × 3)
⇒ $5395.5 = P (1 + 3 × 3/100)
⇒ $5395.5 = P (1 + 9/100)
⇒ $5395.5 = P (100 + 9/100)
⇒ $5395.5 = P × 109/100
⇒ P × 109/100 = $5395.5
⇒ P = 5395.5/109/100
⇒ P = 5395.5 × 100/109
⇒ P = 5395.5 × 100/109
⇒ P = 539550/109
⇒ P = $4950
Thus, the sum borrowed (P) = $4950 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 5395.5, then the Principal = 100/109 × 5395.5
= 100 × 5395.5/109
= 539550/109
= 4950
Thus, Principal = $4950
Thus, the sum borrowed = $4950 Answer
Similar Questions
(1) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 4 years.
(2) How much loan did Charles borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6785 to clear it?
(3) Donna had to pay $5141 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $10200 to clear the loan, then find the time period of the loan.
(5) Karen had to pay $4424 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.
(7) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(8) If Kenneth paid $6000 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) If Susan paid $3942 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) If Donald paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.