Question:
If John paid $3584 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$3200
Solution And Explanation
Solution
Given,
Amount (A) = $3584
Rate of Simple Interest (R) = 3%
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
$3584 = P (1 + 3% × 4)
⇒ $3584 = P (1 + 3/100 × 4)
⇒ $3584 = P (1 + 3 × 4/100)
⇒ $3584 = P (1 + 12/100)
⇒ $3584 = P (100 + 12/100)
⇒ $3584 = P × 112/100
⇒ P × 112/100 = $3584
⇒ P = 3584/112/100
⇒ P = 3584 × 100/112
⇒ P = 3584 × 100/112
⇒ P = 358400/112
⇒ P = $3200
Thus, the sum borrowed (P) = $3200 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 12
Thus, simple interest for 4 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 3584, then the Principal = 100/112 × 3584
= 100 × 3584/112
= 358400/112
= 3200
Thus, Principal = $3200
Thus, the sum borrowed = $3200 Answer
Similar Questions
(1) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 7 years.
(2) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.
(3) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 6% simple interest?
(4) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 7 years.
(5) How much loan did Mark borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7040 to clear it?
(6) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.
(7) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 5% simple interest?
(8) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 3 years.
(9) Robert had to pay $3286 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 8 years.