Question:
How much loan did Stephanie borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8682.5 to clear it?
Correct Answer
$7550
Solution And Explanation
Solution
Given,
Amount (A) = $8682.5
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
$8682.5 = P (1 + 3% × 5)
⇒ $8682.5 = P (1 + 3/100 × 5)
⇒ $8682.5 = P (1 + 3 × 5/100)
⇒ $8682.5 = P (1 + 15/100)
⇒ $8682.5 = P (100 + 15/100)
⇒ $8682.5 = P × 115/100
⇒ P × 115/100 = $8682.5
⇒ P = 8682.5/115/100
⇒ P = 8682.5 × 100/115
⇒ P = 8682.5 × 100/115
⇒ P = 868250/115
⇒ P = $7550
Thus, the sum borrowed (P) = $7550 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 8682.5, then the Principal = 100/115 × 8682.5
= 100 × 8682.5/115
= 868250/115
= 7550
Thus, Principal = $7550
Thus, the sum borrowed = $7550 Answer
Similar Questions
(1) Find the amount to be paid if Thomas borrowed a sum of $5800 at 2% simple interest for 8 years.
(2) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 4% simple interest.
(3) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 4% simple interest?
(4) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 8 years.
(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 7 years.
(6) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 8 years.
(7) If Karen paid $4266 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(9) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $10498 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 3 years.