Question:
How much loan did Sandra borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7095 to clear it?
Correct Answer
$6450
Solution And Explanation
Solution
Given,
Amount (A) = $7095
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
$7095 = P (1 + 2% × 5)
⇒ $7095 = P (1 + 2/100 × 5)
⇒ $7095 = P (1 + 2 × 5/100)
⇒ $7095 = P (1 + 10/100)
⇒ $7095 = P (100 + 10/100)
⇒ $7095 = P × 110/100
⇒ P × 110/100 = $7095
⇒ P = 7095/110/100
⇒ P = 7095 × 100/110
⇒ P = 7095 × 100/110
⇒ P = 709500/110
⇒ P = $6450
Thus, the sum borrowed (P) = $6450 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 7095, then the Principal = 100/110 × 7095
= 100 × 7095/110
= 709500/110
= 6450
Thus, Principal = $6450
Thus, the sum borrowed = $6450 Answer
Similar Questions
(1) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 7 years.
(2) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 3 years.
(4) Find the amount to be paid if John borrowed a sum of $5200 at 8% simple interest for 8 years.
(5) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 7% simple interest?
(6) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5576 to clear the loan, then find the time period of the loan.
(7) Paul had to pay $4982 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 7 years.
(9) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 4 years.
(10) Linda had to pay $3551 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.