Question:
How much loan did Jacob borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9600 to clear it?
Correct Answer
$8000
Solution And Explanation
Solution
Given,
Amount (A) = $9600
Rate of Simple Interest (R) = 4%
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
$9600 = P (1 + 4% × 5)
⇒ $9600 = P (1 + 4/100 × 5)
⇒ $9600 = P (1 + 4 × 5/100)
⇒ $9600 = P (1 + 20/100)
⇒ $9600 = P (100 + 20/100)
⇒ $9600 = P × 120/100
⇒ P × 120/100 = $9600
⇒ P = 9600/120/100
⇒ P = 9600 × 100/120
⇒ P = 9600 × 100/120
⇒ P = 960000/120
⇒ 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 20
Thus, simple interest for 5 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 9600, then the Principal = 100/120 × 9600
= 100 × 9600/120
= 960000/120
= 8000
Thus, Principal = $8000
Thus, the sum borrowed = $8000 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
(2) If Matthew paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.
(4) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 8% simple interest?
(5) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 6% simple interest?
(6) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 4 years.
(7) Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 4 years.
(8) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
(9) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 10% simple interest?
(10) Jennifer took a loan of $4500 at the rate of 8% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.