Question:
Matthew had to pay $4830 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
Correct Answer
$4200
Solution And Explanation
Solution
Given,
Amount (A) = $4830
Rate of Simple Interest (R) = 5%
Time (T) = 3 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
$4830 = P (1 + 5% × 3)
⇒ $4830 = P (1 + 5/100 × 3)
⇒ $4830 = P (1 + 5 × 3/100)
⇒ $4830 = P (1 + 15/100)
⇒ $4830 = P (100 + 15/100)
⇒ $4830 = P × 115/100
⇒ P × 115/100 = $4830
⇒ P = 4830/115/100
⇒ P = 4830 × 100/115
⇒ P = 4830 × 100/115
⇒ P = 483000/115
⇒ P = $4200
Thus, the sum borrowed (P) = $4200 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
Calculation of the Amount
Since, in the question, time = 3 years
So, we need to calculate the simple interest for the given time period, which is 3 years
Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year
= 3 × 5 = 15
Thus, simple interest for 3 years = 15
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 15 = 115
Calculation of the Principal
Now,
∵ If the Amount is 115, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/115
∴ If the Amount is 4830, then the Principal = 100/115 × 4830
= 100 × 4830/115
= 483000/115
= 4200
Thus, Principal = $4200
Thus, the sum borrowed = $4200 Answer
Similar Questions
(1) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 8 years.
(2) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.
(4) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
(5) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Michael borrowed a sum of $3300 at 4% simple interest for 3 years.
(7) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.
(8) If Richard paid $4032 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) If Sarah borrowed $3850 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 7% simple interest?