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) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
(2) If David paid $3672 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $13110 to clear the loan, then find the time period of the loan.
(4) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 3 years.
(6) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.
(7) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11868 to clear the loan, then find the time period of the loan.
(8) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $12000 to clear the loan, then find the time period of the loan.
(9) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 6% simple interest?
(10) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.