Question:
David had to pay $3604 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
Correct Answer
$3400
Solution And Explanation
Solution
Given,
Amount (A) = $3604
Rate of Simple Interest (R) = 2%
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
$3604 = P (1 + 2% × 3)
⇒ $3604 = P (1 + 2/100 × 3)
⇒ $3604 = P (1 + 2 × 3/100)
⇒ $3604 = P (1 + 6/100)
⇒ $3604 = P (100 + 6/100)
⇒ $3604 = P × 106/100
⇒ P × 106/100 = $3604
⇒ P = 3604/106/100
⇒ P = 3604 × 100/106
⇒ P = 3604 × 100/106
⇒ P = 360400/106
⇒ P = $3400
Thus, the sum borrowed (P) = $3400 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 6
Thus, simple interest for 3 years = 6
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 6 = 106
Calculation of the Principal
Now,
∵ If the Amount is 106, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/106
∴ If the Amount is 3604, then the Principal = 100/106 × 3604
= 100 × 3604/106
= 360400/106
= 3400
Thus, Principal = $3400
Thus, the sum borrowed = $3400 Answer
Similar Questions
(1) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 7 years.
(2) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 7 years.
(3) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 3% simple interest?
(4) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 4 years.
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 7 years.
(6) 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.
(7) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.
(8) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 9% simple interest?
(9) How much loan did George borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8395 to clear it?
(10) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 3 years.