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) In how much time a principal of $3100 will amount to $3224 at a simple interest of 2% per annum?
(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 7 years.
(3) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 10% simple interest?
(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 3 years.
(5) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.
(7) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.
(8) What amount will be due after 2 years if James borrowed a sum of $3000 at a 5% simple interest?
(9) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 7 years.
(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 3 years.