Question:
How much loan did Joseph borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6270 to clear it?
Correct Answer
$5700
Solution And Explanation
Solution
Given,
Amount (A) = $6270
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
$6270 = P (1 + 2% × 5)
⇒ $6270 = P (1 + 2/100 × 5)
⇒ $6270 = P (1 + 2 × 5/100)
⇒ $6270 = P (1 + 10/100)
⇒ $6270 = P (100 + 10/100)
⇒ $6270 = P × 110/100
⇒ P × 110/100 = $6270
⇒ P = 6270/110/100
⇒ P = 6270 × 100/110
⇒ P = 6270 × 100/110
⇒ P = 627000/110
⇒ P = $5700
Thus, the sum borrowed (P) = $5700 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 6270, then the Principal = 100/110 × 6270
= 100 × 6270/110
= 627000/110
= 5700
Thus, Principal = $5700
Thus, the sum borrowed = $5700 Answer
Similar Questions
(1) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(2) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 2% simple interest?
(3) 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?
(4) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 4% simple interest?
(5) Calculate the amount due if John borrowed a sum of $3200 at 4% simple interest for 3 years.
(6) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.
(7) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 3% simple interest?
(8) If Richard borrowed $3600 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(9) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 4% simple interest?
(10) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10332 to clear the loan, then find the time period of the loan.