Question:
If Betty paid $4930 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$4250
Solution And Explanation
Solution
Given,
Amount (A) = $4930
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
$4930 = P (1 + 4% × 4)
⇒ $4930 = P (1 + 4/100 × 4)
⇒ $4930 = P (1 + 4 × 4/100)
⇒ $4930 = P (1 + 16/100)
⇒ $4930 = P (100 + 16/100)
⇒ $4930 = P × 116/100
⇒ P × 116/100 = $4930
⇒ P = 4930/116/100
⇒ P = 4930 × 100/116
⇒ P = 4930 × 100/116
⇒ P = 493000/116
⇒ P = $4250
Thus, the sum borrowed (P) = $4250 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 4930, then the Principal = 100/116 × 4930
= 100 × 4930/116
= 493000/116
= 4250
Thus, Principal = $4250
Thus, the sum borrowed = $4250 Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.
(2) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 3% simple interest?
(3) If Charles borrowed $3900 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(4) How much loan did Emily borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7762.5 to clear it?
(5) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 3 years.
(6) How much loan did Margaret borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7937.5 to clear it?
(7) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 4% simple interest?
(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 8 years.
(9) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 8 years.
(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 8 years.