Question:
How much loan did Richard borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6160 to clear it?
Correct Answer
$5600
Solution And Explanation
Solution
Given,
Amount (A) = $6160
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
$6160 = P (1 + 2% × 5)
⇒ $6160 = P (1 + 2/100 × 5)
⇒ $6160 = P (1 + 2 × 5/100)
⇒ $6160 = P (1 + 10/100)
⇒ $6160 = P (100 + 10/100)
⇒ $6160 = P × 110/100
⇒ P × 110/100 = $6160
⇒ P = 6160/110/100
⇒ P = 6160 × 100/110
⇒ P = 6160 × 100/110
⇒ P = 616000/110
⇒ P = $5600
Thus, the sum borrowed (P) = $5600 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 6160, then the Principal = 100/110 × 6160
= 100 × 6160/110
= 616000/110
= 5600
Thus, Principal = $5600
Thus, the sum borrowed = $5600 Answer
Similar Questions
(1) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(2) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(3) James had to pay $3180 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 6% simple interest?
(5) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.
(6) Daniel had to pay $4592 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 7% simple interest?
(8) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(9) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 3 years.