Question:
How much loan did Charles borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7375 to clear it?
Correct Answer
$5900
Solution And Explanation
Solution
Given,
Amount (A) = $7375
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
$7375 = P (1 + 5% × 5)
⇒ $7375 = P (1 + 5/100 × 5)
⇒ $7375 = P (1 + 5 × 5/100)
⇒ $7375 = P (1 + 25/100)
⇒ $7375 = P (100 + 25/100)
⇒ $7375 = P × 125/100
⇒ P × 125/100 = $7375
⇒ P = 7375/125/100
⇒ P = 7375 × 100/125
⇒ P = 7375 × 100/125
⇒ P = 737500/125
⇒ P = $5900
Thus, the sum borrowed (P) = $5900 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 7375, then the Principal = 100/125 × 7375
= 100 × 7375/125
= 737500/125
= 5900
Thus, Principal = $5900
Thus, the sum borrowed = $5900 Answer
Similar Questions
(1) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 4 years.
(2) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 7 years.
(3) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(4) If Sandra paid $5162 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 8 years.
(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 4 years.
(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 8 years.
(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 8 years.
(9) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11041 to clear the loan, then find the time period of the loan.
(10) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8428 to clear the loan, then find the time period of the loan.