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) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 4 years.
(3) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 3% simple interest.
(4) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 8 years.
(5) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 2% simple interest?
(6) How much loan did Amanda borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8580 to clear it?
(7) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 9% simple interest?
(8) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 8% simple interest?
(9) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 6% simple interest?
(10) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 5% simple interest?