Question:
If Michael paid $3828 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3300
Solution And Explanation
Solution
Given,
Amount (A) = $3828
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
$3828 = P (1 + 4% × 4)
⇒ $3828 = P (1 + 4/100 × 4)
⇒ $3828 = P (1 + 4 × 4/100)
⇒ $3828 = P (1 + 16/100)
⇒ $3828 = P (100 + 16/100)
⇒ $3828 = P × 116/100
⇒ P × 116/100 = $3828
⇒ P = 3828/116/100
⇒ P = 3828 × 100/116
⇒ P = 3828 × 100/116
⇒ P = 382800/116
⇒ P = $3300
Thus, the sum borrowed (P) = $3300 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 3828, then the Principal = 100/116 × 3828
= 100 × 3828/116
= 382800/116
= 3300
Thus, Principal = $3300
Thus, the sum borrowed = $3300 Answer
Similar Questions
(1) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 6% simple interest?
(2) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 4 years.
(3) What amount does William have to pay after 5 years if he takes a loan of $3500 at 3% simple interest?
(4) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(5) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 4 years.
(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 9% simple interest for 8 years.
(7) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 4 years.
(8) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
(9) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 9% simple interest?
(10) If Patricia borrowed $3150 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.