Question:
How much loan did Brian borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7920 to clear it?
Correct Answer
$7200
Solution And Explanation
Solution
Given,
Amount (A) = $7920
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
$7920 = P (1 + 2% × 5)
⇒ $7920 = P (1 + 2/100 × 5)
⇒ $7920 = P (1 + 2 × 5/100)
⇒ $7920 = P (1 + 10/100)
⇒ $7920 = P (100 + 10/100)
⇒ $7920 = P × 110/100
⇒ P × 110/100 = $7920
⇒ P = 7920/110/100
⇒ P = 7920 × 100/110
⇒ P = 7920 × 100/110
⇒ P = 792000/110
⇒ P = $7200
Thus, the sum borrowed (P) = $7200 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 7920, then the Principal = 100/110 × 7920
= 100 × 7920/110
= 792000/110
= 7200
Thus, Principal = $7200
Thus, the sum borrowed = $7200 Answer
Similar Questions
(1) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 6% simple interest?
(2) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.
(3) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 5% simple interest?
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 7 years.
(5) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 5% simple interest.
(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 4 years.
(7) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 7 years.
(9) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
(10) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 10% simple interest?