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 Patricia borrowed a sum of $3150 at 3% simple interest for 3 years.
(2) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 3 years.
(3) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11222 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 6% simple interest for 8 years.
(5) In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?
(6) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
(8) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 3 years.
(10) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $12730 to clear the loan, then find the time period of the loan.