Question:
If Anthony paid $4644 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$4300
Solution And Explanation
Solution
Given,
Amount (A) = $4644
Rate of Simple Interest (R) = 2%
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
$4644 = P (1 + 2% × 4)
⇒ $4644 = P (1 + 2/100 × 4)
⇒ $4644 = P (1 + 2 × 4/100)
⇒ $4644 = P (1 + 8/100)
⇒ $4644 = P (100 + 8/100)
⇒ $4644 = P × 108/100
⇒ P × 108/100 = $4644
⇒ P = 4644/108/100
⇒ P = 4644 × 100/108
⇒ P = 4644 × 100/108
⇒ P = 464400/108
⇒ P = $4300
Thus, the sum borrowed (P) = $4300 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 8
Thus, simple interest for 4 years = 8
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 8 = 108
Calculation of the Principal
Now,
∵ If the Amount is 108, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/108
∴ If the Amount is 4644, then the Principal = 100/108 × 4644
= 100 × 4644/108
= 464400/108
= 4300
Thus, Principal = $4300
Thus, the sum borrowed = $4300 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.
(3) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 5% simple interest?
(4) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 7 years.
(5) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.
(6) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 3% simple interest?
(7) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 4 years.
(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 4% simple interest for 8 years.
(9) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
(10) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 4 years.