Question:
( 1 of 10 ) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?
(A) 59
(B) 30.5
(C) 61
(D) 60
You selected
$6984.38
Correct Answer
$7450
Solution And Explanation
Solution
Given,
Amount (A) = $9312.5
Rate of Simple Interest (R) = 5%
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
$9312.5 = P (1 + 5% × 5)
⇒ $9312.5 = P (1 + 5/100 × 5)
⇒ $9312.5 = P (1 + 5 × 5/100)
⇒ $9312.5 = P (1 + 25/100)
⇒ $9312.5 = P (100 + 25/100)
⇒ $9312.5 = P × 125/100
⇒ P × 125/100 = $9312.5
⇒ P = 9312.5/125/100
⇒ P = 9312.5 × 100/125
⇒ P = 9312.5 × 100/125
⇒ P = 931250/125
⇒ P = $7450
Thus, the sum borrowed (P) = $7450 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 = 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 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 9312.5, then the Principal = 100/125 × 9312.5
= 100 × 9312.5/125
= 931250/125
= 7450
Thus, Principal = $7450
Thus, the sum borrowed = $7450 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.
(2) Calculate the amount due if Jessica borrowed a sum of $3750 at 2% simple interest for 4 years.
(3) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 4% simple interest?
(4) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 3 years.
(5) In how much time a principal of $3000 will amount to $3450 at a simple interest of 3% per annum?
(6) What amount will be due after 2 years if David borrowed a sum of $3200 at a 4% simple interest?
(7) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8750 to clear it?
(8) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 7 years.
(9) Ashley had to pay $4959.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.