Question:
How much loan did Jacob borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8800 to clear it?
Correct Answer
$8000
Solution And Explanation
Solution
Given,
Amount (A) = $8800
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
$8800 = P (1 + 2% × 5)
⇒ $8800 = P (1 + 2/100 × 5)
⇒ $8800 = P (1 + 2 × 5/100)
⇒ $8800 = P (1 + 10/100)
⇒ $8800 = P (100 + 10/100)
⇒ $8800 = P × 110/100
⇒ P × 110/100 = $8800
⇒ P = 8800/110/100
⇒ P = 8800 × 100/110
⇒ P = 8800 × 100/110
⇒ P = 880000/110
⇒ P = $8000
Thus, the sum borrowed (P) = $8000 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 8800, then the Principal = 100/110 × 8800
= 100 × 8800/110
= 880000/110
= 8000
Thus, Principal = $8000
Thus, the sum borrowed = $8000 Answer
Similar Questions
(1) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 4 years.
(3) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 9% simple interest.
(5) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 4% simple interest?
(6) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 4 years.
(7) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(8) If Richard paid $4176 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) If Sarah paid $4620 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 7 years.