Question:
( 1 of 10 ) How much loan did Paul borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8040 to clear it?
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
$6030
Correct Answer
$6700
Solution And Explanation
Solution
Given,
Amount (A) = $8040
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
$8040 = P (1 + 4% × 5)
⇒ $8040 = P (1 + 4/100 × 5)
⇒ $8040 = P (1 + 4 × 5/100)
⇒ $8040 = P (1 + 20/100)
⇒ $8040 = P (100 + 20/100)
⇒ $8040 = P × 120/100
⇒ P × 120/100 = $8040
⇒ P = 8040/120/100
⇒ P = 8040 × 100/120
⇒ P = 8040 × 100/120
⇒ P = 804000/120
⇒ P = $6700
Thus, the sum borrowed (P) = $6700 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 8040, then the Principal = 100/120 × 8040
= 100 × 8040/120
= 804000/120
= 6700
Thus, Principal = $6700
Thus, the sum borrowed = $6700 Answer
Similar Questions
(1) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.
(2) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 4% simple interest?
(3) In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?
(4) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.
(5) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 4 years.
(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 7 years.
(7) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 8 years.
(8) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6812.5 to clear it?
(9) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 5% simple interest.