Question:
How much loan did Charles borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6490 to clear it?
Correct Answer
$5900
Solution And Explanation
Solution
Given,
Amount (A) = $6490
Rate of Simple Interest (R) = 2%
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
$6490 = P (1 + 2% × 5)
⇒ $6490 = P (1 + 2/100 × 5)
⇒ $6490 = P (1 + 2 × 5/100)
⇒ $6490 = P (1 + 10/100)
⇒ $6490 = P (100 + 10/100)
⇒ $6490 = P × 110/100
⇒ P × 110/100 = $6490
⇒ P = 6490/110/100
⇒ P = 6490 × 100/110
⇒ P = 6490 × 100/110
⇒ P = 649000/110
⇒ 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 6490, then the Principal = 100/110 × 6490
= 100 × 6490/110
= 649000/110
= 5900
Thus, Principal = $5900
Thus, the sum borrowed = $5900 Answer
Similar Questions
(1) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 8 years.
(2) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 4 years.
(3) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 7 years.
(4) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?
(5) How much loan did Lisa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6957.5 to clear it?
(6) What amount does David have to pay after 5 years if he takes a loan of $3400 at 9% simple interest?
(7) In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?
(8) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.
(9) Nancy had to pay $4399 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 3 years.