Question:
( 1 of 10 ) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8797.5 to clear it?
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
$6598.13
Correct Answer
$7650
Solution And Explanation
Solution
Given,
Amount (A) = $8797.5
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
$8797.5 = P (1 + 3% × 5)
⇒ $8797.5 = P (1 + 3/100 × 5)
⇒ $8797.5 = P (1 + 3 × 5/100)
⇒ $8797.5 = P (1 + 15/100)
⇒ $8797.5 = P (100 + 15/100)
⇒ $8797.5 = P × 115/100
⇒ P × 115/100 = $8797.5
⇒ P = 8797.5/115/100
⇒ P = 8797.5 × 100/115
⇒ P = 8797.5 × 100/115
⇒ P = 879750/115
⇒ P = $7650
Thus, the sum borrowed (P) = $7650 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 8797.5, then the Principal = 100/115 × 8797.5
= 100 × 8797.5/115
= 879750/115
= 7650
Thus, Principal = $7650
Thus, the sum borrowed = $7650 Answer
Similar Questions
(1) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 3 years.
(2) If Mary paid $3294 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 4 years.
(5) Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 8 years.
(6) In how much time a principal of $3150 will amount to $3937.5 at a simple interest of 5% per annum?
(7) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.
(8) How much loan did Michelle borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8687.5 to clear it?
(9) What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 9% simple interest?
(10) If Michelle paid $5940 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.