Question:
James had to pay $3270 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
$3000
Solution And Explanation
Solution
Given,
Amount (A) = $3270
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
$3270 = P (1 + 3% × 3)
⇒ $3270 = P (1 + 3/100 × 3)
⇒ $3270 = P (1 + 3 × 3/100)
⇒ $3270 = P (1 + 9/100)
⇒ $3270 = P (100 + 9/100)
⇒ $3270 = P × 109/100
⇒ P × 109/100 = $3270
⇒ P = 3270/109/100
⇒ P = 3270 × 100/109
⇒ P = 3270 × 100/109
⇒ P = 327000/109
⇒ P = $3000
Thus, the sum borrowed (P) = $3000 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 3270, then the Principal = 100/109 × 3270
= 100 × 3270/109
= 327000/109
= 3000
Thus, Principal = $3000
Thus, the sum borrowed = $3000 Answer
Similar Questions
(1) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 4% simple interest?
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 8 years.
(3) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $7680 to clear the loan, then find the time period of the loan.
(4) Daniel had to pay $4346 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 5% simple interest?
(7) If Michael paid $3960 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.
(10) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.