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 Anthony paid $4644 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) How much loan did Ryan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9085 to clear it?
(3) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
(4) How much loan did Melissa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8085 to clear it?
(5) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $5984 to clear the loan, then find the time period of the loan.
(6) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 6% simple interest?
(7) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 7 years.
(9) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.
(10) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 2% simple interest?