Question:
How much loan did David borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6480 to clear it?
Correct Answer
$5400
Solution And Explanation
Solution
Given,
Amount (A) = $6480
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
$6480 = P (1 + 4% × 5)
⇒ $6480 = P (1 + 4/100 × 5)
⇒ $6480 = P (1 + 4 × 5/100)
⇒ $6480 = P (1 + 20/100)
⇒ $6480 = P (100 + 20/100)
⇒ $6480 = P × 120/100
⇒ P × 120/100 = $6480
⇒ P = 6480/120/100
⇒ P = 6480 × 100/120
⇒ P = 6480 × 100/120
⇒ P = 648000/120
⇒ P = $5400
Thus, the sum borrowed (P) = $5400 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 6480, then the Principal = 100/120 × 6480
= 100 × 6480/120
= 648000/120
= 5400
Thus, Principal = $5400
Thus, the sum borrowed = $5400 Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.
(2) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 10% simple interest?
(3) How much loan did Jacob borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9600 to clear it?
(4) Robert had to pay $3472 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 8 years.
(6) In how much time a principal of $3200 will amount to $3680 at a simple interest of 5% per annum?
(7) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.
(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 3 years.
(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 8 years.
(10) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 8 years.