Question:
Patricia had to pay $3622.5 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
$3150
Solution And Explanation
Solution
Given,
Amount (A) = $3622.5
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
$3622.5 = P (1 + 5% × 3)
⇒ $3622.5 = P (1 + 5/100 × 3)
⇒ $3622.5 = P (1 + 5 × 3/100)
⇒ $3622.5 = P (1 + 15/100)
⇒ $3622.5 = P (100 + 15/100)
⇒ $3622.5 = P × 115/100
⇒ P × 115/100 = $3622.5
⇒ P = 3622.5/115/100
⇒ P = 3622.5 × 100/115
⇒ P = 3622.5 × 100/115
⇒ P = 362250/115
⇒ P = $3150
Thus, the sum borrowed (P) = $3150 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 3622.5, then the Principal = 100/115 × 3622.5
= 100 × 3622.5/115
= 362250/115
= 3150
Thus, Principal = $3150
Thus, the sum borrowed = $3150 Answer
Similar Questions
(1) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 8% simple interest?
(2) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 4% simple interest?
(4) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.
(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 7 years.
(6) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 3% simple interest?
(7) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 3 years.
(8) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 3 years.
(9) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 8% simple interest?
(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 4 years.