Question:
How much loan did Sharon borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8912.5 to clear it?
Correct Answer
$7750
Solution And Explanation
Solution
Given,
Amount (A) = $8912.5
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
$8912.5 = P (1 + 3% × 5)
⇒ $8912.5 = P (1 + 3/100 × 5)
⇒ $8912.5 = P (1 + 3 × 5/100)
⇒ $8912.5 = P (1 + 15/100)
⇒ $8912.5 = P (100 + 15/100)
⇒ $8912.5 = P × 115/100
⇒ P × 115/100 = $8912.5
⇒ P = 8912.5/115/100
⇒ P = 8912.5 × 100/115
⇒ P = 8912.5 × 100/115
⇒ P = 891250/115
⇒ P = $7750
Thus, the sum borrowed (P) = $7750 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 8912.5, then the Principal = 100/115 × 8912.5
= 100 × 8912.5/115
= 891250/115
= 7750
Thus, Principal = $7750
Thus, the sum borrowed = $7750 Answer
Similar Questions
(1) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 8 years.
(2) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $13000 to clear the loan, then find the time period of the loan.
(3) How much loan did Barbara borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6660 to clear it?
(4) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 8 years.
(5) If Richard paid $3888 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 7 years.
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 8 years.
(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 7 years.
(9) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.