Question:
If Mary paid $3538 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3050
Solution And Explanation
Solution
Given,
Amount (A) = $3538
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
$3538 = P (1 + 4% × 4)
⇒ $3538 = P (1 + 4/100 × 4)
⇒ $3538 = P (1 + 4 × 4/100)
⇒ $3538 = P (1 + 16/100)
⇒ $3538 = P (100 + 16/100)
⇒ $3538 = P × 116/100
⇒ P × 116/100 = $3538
⇒ P = 3538/116/100
⇒ P = 3538 × 100/116
⇒ P = 3538 × 100/116
⇒ P = 353800/116
⇒ P = $3050
Thus, the sum borrowed (P) = $3050 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 3538, then the Principal = 100/116 × 3538
= 100 × 3538/116
= 353800/116
= 3050
Thus, Principal = $3050
Thus, the sum borrowed = $3050 Answer
Similar Questions
(1) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 4% simple interest?
(2) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 2% simple interest?
(3) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.
(4) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 3 years.
(5) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 4% simple interest for 8 years.
(6) Jessica had to pay $3975 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 Charles borrowed a sum of $5900 at 5% simple interest for 7 years.
(8) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.
(10) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.