Question:
How much loan did Amanda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8222.5 to clear it?
Correct Answer
$7150
Solution And Explanation
Solution
Given,
Amount (A) = $8222.5
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
$8222.5 = P (1 + 3% × 5)
⇒ $8222.5 = P (1 + 3/100 × 5)
⇒ $8222.5 = P (1 + 3 × 5/100)
⇒ $8222.5 = P (1 + 15/100)
⇒ $8222.5 = P (100 + 15/100)
⇒ $8222.5 = P × 115/100
⇒ P × 115/100 = $8222.5
⇒ P = 8222.5/115/100
⇒ P = 8222.5 × 100/115
⇒ P = 8222.5 × 100/115
⇒ P = 822250/115
⇒ P = $7150
Thus, the sum borrowed (P) = $7150 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 8222.5, then the Principal = 100/115 × 8222.5
= 100 × 8222.5/115
= 822250/115
= 7150
Thus, Principal = $7150
Thus, the sum borrowed = $7150 Answer
Similar Questions
(1) How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?
(2) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10988 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Jennifer borrowed a sum of $3250 at 8% simple interest for 3 years.
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 9% simple interest for 7 years.
(5) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.
(6) In how much time a principal of $3100 will amount to $3596 at a simple interest of 4% per annum?
(7) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 3 years.
(8) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 9% simple interest?
(9) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $10430 to clear the loan, then find the time period of the loan.
(10) If Thomas borrowed $3800 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.