Question:
If Paul paid $5076 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$4700
Solution And Explanation
Solution
Given,
Amount (A) = $5076
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
$5076 = P (1 + 2% × 4)
⇒ $5076 = P (1 + 2/100 × 4)
⇒ $5076 = P (1 + 2 × 4/100)
⇒ $5076 = P (1 + 8/100)
⇒ $5076 = P (100 + 8/100)
⇒ $5076 = P × 108/100
⇒ P × 108/100 = $5076
⇒ P = 5076/108/100
⇒ P = 5076 × 100/108
⇒ P = 5076 × 100/108
⇒ P = 507600/108
⇒ P = $4700
Thus, the sum borrowed (P) = $4700 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 5076, then the Principal = 100/108 × 5076
= 100 × 5076/108
= 507600/108
= 4700
Thus, Principal = $4700
Thus, the sum borrowed = $4700 Answer
Similar Questions
(1) Donald had to pay $5040 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(3) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 3 years.
(5) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.
(6) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 8% simple interest.
(7) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 5% simple interest.
(8) Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 8 years.
(9) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
(10) What amount does David have to pay after 6 years if he takes a loan of $3400 at 10% simple interest?