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) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.
(2) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9955 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 8 years.
(4) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
(5) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.
(7) How much loan did Christopher borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7500 to clear it?
(8) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 4% simple interest?
(9) William took a loan of $5000 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.
(10) If Elizabeth paid $3864 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.