Question:
How much loan did Melissa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8452.5 to clear it?
Correct Answer
$7350
Solution And Explanation
Solution
Given,
Amount (A) = $8452.5
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
$8452.5 = P (1 + 3% × 5)
⇒ $8452.5 = P (1 + 3/100 × 5)
⇒ $8452.5 = P (1 + 3 × 5/100)
⇒ $8452.5 = P (1 + 15/100)
⇒ $8452.5 = P (100 + 15/100)
⇒ $8452.5 = P × 115/100
⇒ P × 115/100 = $8452.5
⇒ P = 8452.5/115/100
⇒ P = 8452.5 × 100/115
⇒ P = 8452.5 × 100/115
⇒ P = 845250/115
⇒ P = $7350
Thus, the sum borrowed (P) = $7350 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 8452.5, then the Principal = 100/115 × 8452.5
= 100 × 8452.5/115
= 845250/115
= 7350
Thus, Principal = $7350
Thus, the sum borrowed = $7350 Answer
Similar Questions
(1) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 8 years.
(2) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 10% simple interest?
(3) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8305 to clear it?
(4) In how much time a principal of $3000 will amount to $3120 at a simple interest of 2% per annum?
(5) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 5% simple interest?
(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 6% simple interest for 3 years.
(7) Find the amount to be paid if Christopher borrowed a sum of $6000 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 8 years.
(9) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.
(10) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.