Question:
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?
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) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.
(2) If Mary paid $3538 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 7% simple interest for 3 years.
(4) If Robert paid $3472 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Barbara had to pay $3976 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 9% simple interest?
(7) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 6% simple interest.
(8) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 8% simple interest?
(9) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.
(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 8 years.