Question:
How much loan did William borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6325 to clear it?
Correct Answer
$5500
Solution And Explanation
Solution
Given,
Amount (A) = $6325
Rate of Simple Interest (R) = 3%
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
$6325 = P (1 + 3% × 5)
⇒ $6325 = P (1 + 3/100 × 5)
⇒ $6325 = P (1 + 3 × 5/100)
⇒ $6325 = P (1 + 15/100)
⇒ $6325 = P (100 + 15/100)
⇒ $6325 = P × 115/100
⇒ P × 115/100 = $6325
⇒ P = 6325/115/100
⇒ P = 6325 × 100/115
⇒ P = 6325 × 100/115
⇒ P = 632500/115
⇒ P = $5500
Thus, the sum borrowed (P) = $5500 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 15
Thus, simple interest for 5 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 6325, then the Principal = 100/115 × 6325
= 100 × 6325/115
= 632500/115
= 5500
Thus, Principal = $5500
Thus, the sum borrowed = $5500 Answer
Similar Questions
(1) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 3 years.
(2) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 5% simple interest?
(3) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?
(4) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.
(5) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 7 years.
(6) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.
(7) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 7% simple interest?
(8) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 3% simple interest?
(9) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 4% simple interest?
(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 3 years.