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 Michael borrowed a sum of $3300 at 9% simple interest for 3 years.
(2) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 3% simple interest?
(3) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 10% simple interest?
(4) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.
(5) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 4% simple interest?
(6) Kenneth had to pay $5750 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) If Emily paid $5510 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 8% simple interest?
(9) Anthony had to pay $4558 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.