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) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 7% simple interest.
(3) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 4 years.
(4) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 6% simple interest?
(5) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 7 years.
(7) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 8 years.
(8) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 9% simple interest?
(9) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 10% simple interest.
(10) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 6% simple interest?