Question:
How much loan did Karen borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6842.5 to clear it?
Correct Answer
$5950
Solution And Explanation
Solution
Given,
Amount (A) = $6842.5
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
$6842.5 = P (1 + 3% × 5)
⇒ $6842.5 = P (1 + 3/100 × 5)
⇒ $6842.5 = P (1 + 3 × 5/100)
⇒ $6842.5 = P (1 + 15/100)
⇒ $6842.5 = P (100 + 15/100)
⇒ $6842.5 = P × 115/100
⇒ P × 115/100 = $6842.5
⇒ P = 6842.5/115/100
⇒ P = 6842.5 × 100/115
⇒ P = 6842.5 × 100/115
⇒ P = 684250/115
⇒ P = $5950
Thus, the sum borrowed (P) = $5950 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 6842.5, then the Principal = 100/115 × 6842.5
= 100 × 6842.5/115
= 684250/115
= 5950
Thus, Principal = $5950
Thus, the sum borrowed = $5950 Answer
Similar Questions
(1) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7897 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 4 years.
(3) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.
(4) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.
(5) How much loan did Ryan borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9875 to clear it?
(6) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.
(7) How much loan did Nancy borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6765 to clear it?
(8) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $13600 to clear the loan, then find the time period of the loan.
(9) How much loan did Timothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9250 to clear it?
(10) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 7% simple interest?