Question:
If John paid $3712 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3200
Solution And Explanation
Solution
Given,
Amount (A) = $3712
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
$3712 = P (1 + 4% × 4)
⇒ $3712 = P (1 + 4/100 × 4)
⇒ $3712 = P (1 + 4 × 4/100)
⇒ $3712 = P (1 + 16/100)
⇒ $3712 = P (100 + 16/100)
⇒ $3712 = P × 116/100
⇒ P × 116/100 = $3712
⇒ P = 3712/116/100
⇒ P = 3712 × 100/116
⇒ P = 3712 × 100/116
⇒ P = 371200/116
⇒ 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 = 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 3712, then the Principal = 100/116 × 3712
= 100 × 3712/116
= 371200/116
= 3200
Thus, Principal = $3200
Thus, the sum borrowed = $3200 Answer
Similar Questions
(1) How much loan did Anthony borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7245 to clear it?
(2) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $9516 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
(4) What amount does James have to pay after 6 years if he takes a loan of $3000 at 2% simple interest?
(5) Richard had to pay $4032 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.
(7) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 6% simple interest?
(8) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.
(9) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.
(10) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8112 to clear the loan, then find the time period of the loan.