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) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 3 years.
(3) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 10% simple interest?
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 7 years.
(5) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.
(6) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 3 years.
(7) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7800 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 7 years.
(9) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10988 to clear the loan, then find the time period of the loan.
(10) How much loan did Michelle borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7992.5 to clear it?