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) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.
(2) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 10% simple interest?
(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 3% simple interest for 8 years.
(4) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $8400 to clear the loan, then find the time period of the loan.
(5) 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.
(6) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 4 years.
(8) Find the amount to be paid if John borrowed a sum of $5200 at 4% simple interest for 8 years.
(9) How much loan did Sarah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7312.5 to clear it?
(10) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.