Question:
( 1 of 10 ) How much loan did Brian borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8640 to clear it?
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
$6480
Correct Answer
$7200
Solution And Explanation
Solution
Given,
Amount (A) = $8640
Rate of Simple Interest (R) = 4%
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
$8640 = P (1 + 4% × 5)
⇒ $8640 = P (1 + 4/100 × 5)
⇒ $8640 = P (1 + 4 × 5/100)
⇒ $8640 = P (1 + 20/100)
⇒ $8640 = P (100 + 20/100)
⇒ $8640 = P × 120/100
⇒ P × 120/100 = $8640
⇒ P = 8640/120/100
⇒ P = 8640 × 100/120
⇒ P = 8640 × 100/120
⇒ P = 864000/120
⇒ 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 8640, then the Principal = 100/120 × 8640
= 100 × 8640/120
= 864000/120
= 7200
Thus, Principal = $7200
Thus, the sum borrowed = $7200 Answer
Similar Questions
(1) How much loan did Sarah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7020 to clear it?
(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 8 years.
(3) In how much time a principal of $3100 will amount to $3720 at a simple interest of 4% per annum?
(4) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(5) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 4 years.
(7) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 6% simple interest?
(8) Mark had to pay $4796 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 8% simple interest?
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 8 years.