Question:
If William paid $4060 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3500
Solution And Explanation
Solution
Given,
Amount (A) = $4060
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
$4060 = P (1 + 4% × 4)
⇒ $4060 = P (1 + 4/100 × 4)
⇒ $4060 = P (1 + 4 × 4/100)
⇒ $4060 = P (1 + 16/100)
⇒ $4060 = P (100 + 16/100)
⇒ $4060 = P × 116/100
⇒ P × 116/100 = $4060
⇒ P = 4060/116/100
⇒ P = 4060 × 100/116
⇒ P = 4060 × 100/116
⇒ P = 406000/116
⇒ P = $3500
Thus, the sum borrowed (P) = $3500 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 4060, then the Principal = 100/116 × 4060
= 100 × 4060/116
= 406000/116
= 3500
Thus, Principal = $3500
Thus, the sum borrowed = $3500 Answer
Similar Questions
(1) Anthony had to pay $4558 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) James had to pay $3180 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) Find the amount to be paid if James borrowed a sum of $5000 at 10% simple interest for 8 years.
(4) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 10% simple interest.
(6) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $8976 to clear the loan, then find the time period of the loan.
(7) Daniel had to pay $4469 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 6% simple interest for 3 years.
(10) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.