Question:
How much loan did Kenneth borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8750 to clear it?
Correct Answer
$7000
Solution And Explanation
Solution
Given,
Amount (A) = $8750
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
$8750 = P (1 + 5% × 5)
⇒ $8750 = P (1 + 5/100 × 5)
⇒ $8750 = P (1 + 5 × 5/100)
⇒ $8750 = P (1 + 25/100)
⇒ $8750 = P (100 + 25/100)
⇒ $8750 = P × 125/100
⇒ P × 125/100 = $8750
⇒ P = 8750/125/100
⇒ P = 8750 × 100/125
⇒ P = 8750 × 100/125
⇒ P = 875000/125
⇒ P = $7000
Thus, the sum borrowed (P) = $7000 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 8750, then the Principal = 100/125 × 8750
= 100 × 8750/125
= 875000/125
= 7000
Thus, Principal = $7000
Thus, the sum borrowed = $7000 Answer
Similar Questions
(1) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 3 years.
(2) What amount does David have to pay after 5 years if he takes a loan of $3400 at 8% simple interest?
(3) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8568 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 7 years.
(5) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 3 years.
(7) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 3 years.
(8) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 4 years.
(9) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.
(10) If Mary paid $3416 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.