Question:
How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?
Correct Answer
$5950
Solution And Explanation
Solution
Given,
Amount (A) = $7437.5
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
$7437.5 = P (1 + 5% × 5)
⇒ $7437.5 = P (1 + 5/100 × 5)
⇒ $7437.5 = P (1 + 5 × 5/100)
⇒ $7437.5 = P (1 + 25/100)
⇒ $7437.5 = P (100 + 25/100)
⇒ $7437.5 = P × 125/100
⇒ P × 125/100 = $7437.5
⇒ P = 7437.5/125/100
⇒ P = 7437.5 × 100/125
⇒ P = 7437.5 × 100/125
⇒ P = 743750/125
⇒ P = $5950
Thus, the sum borrowed (P) = $5950 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 7437.5, then the Principal = 100/125 × 7437.5
= 100 × 7437.5/125
= 743750/125
= 5950
Thus, Principal = $5950
Thus, the sum borrowed = $5950 Answer
Similar Questions
(1) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 3 years.
(2) In how much time a principal of $3050 will amount to $3294 at a simple interest of 2% per annum?
(3) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 7 years.
(4) How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?
(5) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 3 years.
(6) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 6% simple interest?
(7) In how much time a principal of $3000 will amount to $3450 at a simple interest of 5% per annum?
(8) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 4 years.
(9) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11403 to clear the loan, then find the time period of the loan.
(10) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.