Question:
Joshua had to pay $5635 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
$4900
Solution And Explanation
Solution
Given,
Amount (A) = $5635
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
$5635 = P (1 + 5% × 3)
⇒ $5635 = P (1 + 5/100 × 3)
⇒ $5635 = P (1 + 5 × 3/100)
⇒ $5635 = P (1 + 15/100)
⇒ $5635 = P (100 + 15/100)
⇒ $5635 = P × 115/100
⇒ P × 115/100 = $5635
⇒ P = 5635/115/100
⇒ P = 5635 × 100/115
⇒ P = 5635 × 100/115
⇒ P = 563500/115
⇒ P = $4900
Thus, the sum borrowed (P) = $4900 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 5635, then the Principal = 100/115 × 5635
= 100 × 5635/115
= 563500/115
= 4900
Thus, Principal = $4900
Thus, the sum borrowed = $4900 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.
(2) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.
(3) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 8 years.
(5) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 7 years.
(7) If Steven paid $5336 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.
(9) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.
(10) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 2% simple interest.