Question:
If Richard paid $4176 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3600
Solution And Explanation
Solution
Given,
Amount (A) = $4176
Rate of Simple Interest (R) = 4%
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
$4176 = P (1 + 4% × 4)
⇒ $4176 = P (1 + 4/100 × 4)
⇒ $4176 = P (1 + 4 × 4/100)
⇒ $4176 = P (1 + 16/100)
⇒ $4176 = P (100 + 16/100)
⇒ $4176 = P × 116/100
⇒ P × 116/100 = $4176
⇒ P = 4176/116/100
⇒ P = 4176 × 100/116
⇒ P = 4176 × 100/116
⇒ P = 417600/116
⇒ 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 = 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 = 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 × 4 = 16
Thus, simple interest for 4 years = 16
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 16 = 116
Calculation of the Principal
Now,
∵ If the Amount is 116, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/116
∴ If the Amount is 4176, then the Principal = 100/116 × 4176
= 100 × 4176/116
= 417600/116
= 3600
Thus, Principal = $3600
Thus, the sum borrowed = $3600 Answer
Similar Questions
(1) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10764 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 4 years.
(3) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?
(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 8 years.
(5) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 9% simple interest?
(6) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 3 years.
(7) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.
(8) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.
(9) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 5% simple interest.
(10) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.