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) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.
(2) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9142.5 to clear it?
(3) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 4 years.
(4) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 4 years.
(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 7 years.
(6) If Charles borrowed $3900 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(7) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 3 years.
(8) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 3% simple interest.
(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 7 years.
(10) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 7% simple interest?