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) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 5% simple interest?
(2) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 4 years.
(3) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 3% simple interest for 7 years.
(5) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 4 years.
(6) If David borrowed $3400 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(8) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(9) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 8 years.