Question:
If Lisa paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$4050
Solution And Explanation
Solution
Given,
Amount (A) = $4698
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
$4698 = P (1 + 4% × 4)
⇒ $4698 = P (1 + 4/100 × 4)
⇒ $4698 = P (1 + 4 × 4/100)
⇒ $4698 = P (1 + 16/100)
⇒ $4698 = P (100 + 16/100)
⇒ $4698 = P × 116/100
⇒ P × 116/100 = $4698
⇒ P = 4698/116/100
⇒ P = 4698 × 100/116
⇒ P = 4698 × 100/116
⇒ P = 469800/116
⇒ P = $4050
Thus, the sum borrowed (P) = $4050 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 4698, then the Principal = 100/116 × 4698
= 100 × 4698/116
= 469800/116
= 4050
Thus, Principal = $4050
Thus, the sum borrowed = $4050 Answer
Similar Questions
(1) Calculate the amount due if Jessica borrowed a sum of $3750 at 3% simple interest for 3 years.
(2) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.
(3) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.
(4) In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?
(5) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.
(6) Jennifer had to pay $3445 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 7 years.
(8) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 4 years.
(9) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $12670 to clear the loan, then find the time period of the loan.
(10) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6300 to clear it?