Question:
How much loan did Steven borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8250 to clear it?
Correct Answer
$6600
Solution And Explanation
Solution
Given,
Amount (A) = $8250
Rate of Simple Interest (R) = 5%
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
$8250 = P (1 + 5% × 5)
⇒ $8250 = P (1 + 5/100 × 5)
⇒ $8250 = P (1 + 5 × 5/100)
⇒ $8250 = P (1 + 25/100)
⇒ $8250 = P (100 + 25/100)
⇒ $8250 = P × 125/100
⇒ P × 125/100 = $8250
⇒ P = 8250/125/100
⇒ P = 8250 × 100/125
⇒ P = 8250 × 100/125
⇒ P = 825000/125
⇒ P = $6600
Thus, the sum borrowed (P) = $6600 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 25
Thus, simple interest for 5 years = 25
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 25 = 125
Calculation of the Principal
Now,
∵ If the Amount is 125, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/125
∴ If the Amount is 8250, then the Principal = 100/125 × 8250
= 100 × 8250/125
= 825000/125
= 6600
Thus, Principal = $6600
Thus, the sum borrowed = $6600 Answer
Similar Questions
(1) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 7% simple interest?
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 3 years.
(3) If Paul paid $5452 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.
(6) Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 8 years.
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 8 years.
(8) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8046 to clear the loan, then find the time period of the loan.
(9) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 10% simple interest?
(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 6% simple interest for 4 years.