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) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 4 years.
(2) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 6% simple interest.
(3) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 3 years.
(4) Donald took a loan of $7000 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.
(5) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.
(6) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 2% simple interest?
(7) How much loan did William borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6600 to clear it?
(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 7 years.
(9) If Charles paid $4212 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 7% simple interest?