Question:
Robert had to pay $3565 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
Correct Answer
$3100
Solution And Explanation
Solution
Given,
Amount (A) = $3565
Rate of Simple Interest (R) = 5%
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
$3565 = P (1 + 5% × 3)
⇒ $3565 = P (1 + 5/100 × 3)
⇒ $3565 = P (1 + 5 × 3/100)
⇒ $3565 = P (1 + 15/100)
⇒ $3565 = P (100 + 15/100)
⇒ $3565 = P × 115/100
⇒ P × 115/100 = $3565
⇒ P = 3565/115/100
⇒ P = 3565 × 100/115
⇒ P = 3565 × 100/115
⇒ P = 356500/115
⇒ P = $3100
Thus, the sum borrowed (P) = $3100 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 15
Thus, simple interest for 3 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 3565, then the Principal = 100/115 × 3565
= 100 × 3565/115
= 356500/115
= 3100
Thus, Principal = $3100
Thus, the sum borrowed = $3100 Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5440 to clear the loan, then find the time period of the loan.
(2) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 7% simple interest?
(3) Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 8 years.
(4) What amount will be due after 2 years if John borrowed a sum of $3100 at a 10% simple interest?
(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 8% simple interest for 7 years.
(6) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.
(7) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 5% simple interest?
(8) How much loan did Ronald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8625 to clear it?
(9) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 4 years.
(10) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.