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) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 6% simple interest.
(2) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 6% simple interest?
(3) John had to pay $3584 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(4) Calculate the amount due if Christopher borrowed a sum of $4000 at 4% simple interest for 4 years.
(5) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 7% simple interest?
(6) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 5% simple interest.
(7) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 3 years.
(8) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 4% simple interest?
(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 8 years.
(10) How much loan did Jessica borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6612.5 to clear it?