Question:
How much loan did Thomas borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6380 to clear it?
Correct Answer
$5800
Solution And Explanation
Solution
Given,
Amount (A) = $6380
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
$6380 = P (1 + 2% × 5)
⇒ $6380 = P (1 + 2/100 × 5)
⇒ $6380 = P (1 + 2 × 5/100)
⇒ $6380 = P (1 + 10/100)
⇒ $6380 = P (100 + 10/100)
⇒ $6380 = P × 110/100
⇒ P × 110/100 = $6380
⇒ P = 6380/110/100
⇒ P = 6380 × 100/110
⇒ P = 6380 × 100/110
⇒ P = 638000/110
⇒ P = $5800
Thus, the sum borrowed (P) = $5800 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 6380, then the Principal = 100/110 × 6380
= 100 × 6380/110
= 638000/110
= 5800
Thus, Principal = $5800
Thus, the sum borrowed = $5800 Answer
Similar Questions
(1) How much loan did Joseph borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6555 to clear it?
(2) What amount will be due after 2 years if William borrowed a sum of $3250 at a 6% simple interest?
(3) In how much time a principal of $3200 will amount to $3584 at a simple interest of 3% per annum?
(4) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 4% simple interest?
(5) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 3 years.
(6) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 3 years.
(7) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.
(8) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(9) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 10% simple interest?
(10) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.