Question:
How much loan did Carol borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8107.5 to clear it?
Correct Answer
$7050
Solution And Explanation
Solution
Given,
Amount (A) = $8107.5
Rate of Simple Interest (R) = 3%
Time (T) = 5 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
$8107.5 = P (1 + 3% × 5)
⇒ $8107.5 = P (1 + 3/100 × 5)
⇒ $8107.5 = P (1 + 3 × 5/100)
⇒ $8107.5 = P (1 + 15/100)
⇒ $8107.5 = P (100 + 15/100)
⇒ $8107.5 = P × 115/100
⇒ P × 115/100 = $8107.5
⇒ P = 8107.5/115/100
⇒ P = 8107.5 × 100/115
⇒ P = 8107.5 × 100/115
⇒ P = 810750/115
⇒ P = $7050
Thus, the sum borrowed (P) = $7050 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 = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 8107.5, then the Principal = 100/115 × 8107.5
= 100 × 8107.5/115
= 810750/115
= 7050
Thus, Principal = $7050
Thus, the sum borrowed = $7050 Answer
Similar Questions
(1) 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.
(2) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 9% simple interest?
(3) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $8360 to clear the loan, then find the time period of the loan.
(4) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.
(5) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 4% simple interest?
(6) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.
(7) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 3% simple interest for 7 years.
(9) What amount does James have to pay after 5 years if he takes a loan of $3000 at 8% simple interest?
(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 8 years.