Question:
How much loan did James borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6250 to clear it?
Correct Answer
$5000
Solution And Explanation
Solution
Given,
Amount (A) = $6250
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
$6250 = P (1 + 5% × 5)
⇒ $6250 = P (1 + 5/100 × 5)
⇒ $6250 = P (1 + 5 × 5/100)
⇒ $6250 = P (1 + 25/100)
⇒ $6250 = P (100 + 25/100)
⇒ $6250 = P × 125/100
⇒ P × 125/100 = $6250
⇒ P = 6250/125/100
⇒ P = 6250 × 100/125
⇒ P = 6250 × 100/125
⇒ P = 625000/125
⇒ P = $5000
Thus, the sum borrowed (P) = $5000 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 6250, then the Principal = 100/125 × 6250
= 100 × 6250/125
= 625000/125
= 5000
Thus, Principal = $5000
Thus, the sum borrowed = $5000 Answer
Similar Questions
(1) If Charles paid $4212 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) If Charles paid $4680 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) What amount does James have to pay after 5 years if he takes a loan of $3000 at 10% simple interest?
(4) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11765 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 7% simple interest.
(6) Find the amount to be paid if Jessica borrowed a sum of $5750 at 4% simple interest for 8 years.
(7) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 6% simple interest?
(8) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 2% simple interest.
(9) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 4 years.
(10) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 5% simple interest?