Question:
( 3 of 10 ) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8337.5 to clear it?
(A) 11 19/46 days or 11.413 days
(B) 22 19/46 days or 22.413 days
(C) 46 days
(D) 23 days
You selected
$6253.13
Correct Answer
$7250
Solution And Explanation
Solution
Given,
Amount (A) = $8337.5
Rate of Simple Interest (R) = 3%
Time (T) = 5 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
$8337.5 = P (1 + 3% × 5)
⇒ $8337.5 = P (1 + 3/100 × 5)
⇒ $8337.5 = P (1 + 3 × 5/100)
⇒ $8337.5 = P (1 + 15/100)
⇒ $8337.5 = P (100 + 15/100)
⇒ $8337.5 = P × 115/100
⇒ P × 115/100 = $8337.5
⇒ P = 8337.5/115/100
⇒ P = 8337.5 × 100/115
⇒ P = 8337.5 × 100/115
⇒ P = 833750/115
⇒ P = $7250
Thus, the sum borrowed (P) = $7250 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
Calculation of the Amount
Since, in the question, time = 5 years
So, we need to calculate the simple interest for the given time period, which is 5 years
Thus, Simple Interest for 5 years = 5 × Simple Interest for 1 year
= 5 × 3 = 15
Thus, simple interest for 5 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 8337.5, then the Principal = 100/115 × 8337.5
= 100 × 8337.5/115
= 833750/115
= 7250
Thus, Principal = $7250
Thus, the sum borrowed = $7250 Answer
Similar Questions
(1) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?
(2) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 8 years.
(4) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 3 years.
(6) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.
(7) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 10% simple interest?
(8) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 4% simple interest?
(9) In how much time a principal of $3200 will amount to $3488 at a simple interest of 3% per annum?
(10) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9348 to clear the loan, then find the time period of the loan.