Question:
If Richard paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$3600
Solution And Explanation
Solution
Given,
Amount (A) = $4320
Rate of Simple Interest (R) = 5%
Time (T) = 4 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
$4320 = P (1 + 5% × 4)
⇒ $4320 = P (1 + 5/100 × 4)
⇒ $4320 = P (1 + 5 × 4/100)
⇒ $4320 = P (1 + 20/100)
⇒ $4320 = P (100 + 20/100)
⇒ $4320 = P × 120/100
⇒ P × 120/100 = $4320
⇒ P = 4320/120/100
⇒ P = 4320 × 100/120
⇒ P = 4320 × 100/120
⇒ P = 432000/120
⇒ P = $3600
Thus, the sum borrowed (P) = $3600 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
Calculation of the Amount
Since, in the question, time = 4 years
So, we need to calculate the simple interest for the given time period, which is 4 years
Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year
= 4 × 5 = 20
Thus, simple interest for 4 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 4320, then the Principal = 100/120 × 4320
= 100 × 4320/120
= 432000/120
= 3600
Thus, Principal = $3600
Thus, the sum borrowed = $3600 Answer
Similar Questions
(1) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 7 years.
(2) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7344 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
(4) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 7 years.
(5) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 2% simple interest?
(6) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 2% simple interest.
(7) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.
(8) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(9) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 7 years.