Question:
How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8580 to clear it?
Correct Answer
$7800
Solution And Explanation
Solution
Given,
Amount (A) = $8580
Rate of Simple Interest (R) = 2%
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
$8580 = P (1 + 2% × 5)
⇒ $8580 = P (1 + 2/100 × 5)
⇒ $8580 = P (1 + 2 × 5/100)
⇒ $8580 = P (1 + 10/100)
⇒ $8580 = P (100 + 10/100)
⇒ $8580 = P × 110/100
⇒ P × 110/100 = $8580
⇒ P = 8580/110/100
⇒ P = 8580 × 100/110
⇒ P = 8580 × 100/110
⇒ P = 858000/110
⇒ P = $7800
Thus, the sum borrowed (P) = $7800 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 10
Thus, simple interest for 5 years = 10
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 10 = 110
Calculation of the Principal
Now,
∵ If the Amount is 110, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/110
∴ If the Amount is 8580, then the Principal = 100/110 × 8580
= 100 × 8580/110
= 858000/110
= 7800
Thus, Principal = $7800
Thus, the sum borrowed = $7800 Answer
Similar Questions
(1) If Karen borrowed $3950 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(2) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 4 years.
(3) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.
(4) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 7% simple interest?
(5) If Thomas borrowed $3800 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(6) What amount does David have to pay after 6 years if he takes a loan of $3400 at 9% simple interest?
(7) Calculate the amount due if Karen borrowed a sum of $3950 at 6% simple interest for 4 years.
(8) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.
(9) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if James borrowed a sum of $3000 at a 9% simple interest?