Question:
If Paul paid $5452 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$4700
Solution And Explanation
Solution
Given,
Amount (A) = $5452
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
$5452 = P (1 + 4% × 4)
⇒ $5452 = P (1 + 4/100 × 4)
⇒ $5452 = P (1 + 4 × 4/100)
⇒ $5452 = P (1 + 16/100)
⇒ $5452 = P (100 + 16/100)
⇒ $5452 = P × 116/100
⇒ P × 116/100 = $5452
⇒ P = 5452/116/100
⇒ P = 5452 × 100/116
⇒ P = 5452 × 100/116
⇒ P = 545200/116
⇒ 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 = 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 5452, then the Principal = 100/116 × 5452
= 100 × 5452/116
= 545200/116
= 4700
Thus, Principal = $4700
Thus, the sum borrowed = $4700 Answer
Similar Questions
(1) What amount does James have to pay after 6 years if he takes a loan of $3000 at 3% simple interest?
(2) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 3 years.
(3) How much loan did Barbara borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6105 to clear it?
(4) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(6) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 8 years.
(7) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 4 years.
(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 2% simple interest for 3 years.
(9) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 10% simple interest?