Question:
Richard had to pay $3816 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
$3600
Solution And Explanation
Solution
Given,
Amount (A) = $3816
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
$3816 = P (1 + 2% × 3)
⇒ $3816 = P (1 + 2/100 × 3)
⇒ $3816 = P (1 + 2 × 3/100)
⇒ $3816 = P (1 + 6/100)
⇒ $3816 = P (100 + 6/100)
⇒ $3816 = P × 106/100
⇒ P × 106/100 = $3816
⇒ P = 3816/106/100
⇒ P = 3816 × 100/106
⇒ P = 3816 × 100/106
⇒ P = 381600/106
⇒ P = $3600
Thus, the sum borrowed (P) = $3600 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 3816, then the Principal = 100/106 × 3816
= 100 × 3816/106
= 381600/106
= 3600
Thus, Principal = $3600
Thus, the sum borrowed = $3600 Answer
Similar Questions
(1) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 8 years.
(2) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.
(4) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.
(5) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.
(6) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 9% simple interest.
(8) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 8% simple interest?
(9) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 6% simple interest.
(10) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 9% simple interest?