Question:
How much loan did Lisa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7562.5 to clear it?
Correct Answer
$6050
Solution And Explanation
Solution
Given,
Amount (A) = $7562.5
Rate of Simple Interest (R) = 5%
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
$7562.5 = P (1 + 5% × 5)
⇒ $7562.5 = P (1 + 5/100 × 5)
⇒ $7562.5 = P (1 + 5 × 5/100)
⇒ $7562.5 = P (1 + 25/100)
⇒ $7562.5 = P (100 + 25/100)
⇒ $7562.5 = P × 125/100
⇒ P × 125/100 = $7562.5
⇒ P = 7562.5/125/100
⇒ P = 7562.5 × 100/125
⇒ P = 7562.5 × 100/125
⇒ P = 756250/125
⇒ P = $6050
Thus, the sum borrowed (P) = $6050 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 7562.5, then the Principal = 100/125 × 7562.5
= 100 × 7562.5/125
= 756250/125
= 6050
Thus, Principal = $6050
Thus, the sum borrowed = $6050 Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5960 to clear the loan, then find the time period of the loan.
(2) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 7% simple interest?
(3) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 6% simple interest?
(4) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.
(5) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 4% simple interest?
(7) In how much time a principal of $3150 will amount to $3433.5 at a simple interest of 3% per annum?
(8) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.
(9) If Michelle paid $5544 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.