Question:
If Joseph paid $3996 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$3700
Solution And Explanation
Solution
Given,
Amount (A) = $3996
Rate of Simple Interest (R) = 2%
Time (T) = 4 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
$3996 = P (1 + 2% × 4)
⇒ $3996 = P (1 + 2/100 × 4)
⇒ $3996 = P (1 + 2 × 4/100)
⇒ $3996 = P (1 + 8/100)
⇒ $3996 = P (100 + 8/100)
⇒ $3996 = P × 108/100
⇒ P × 108/100 = $3996
⇒ P = 3996/108/100
⇒ P = 3996 × 100/108
⇒ P = 3996 × 100/108
⇒ P = 399600/108
⇒ P = $3700
Thus, the sum borrowed (P) = $3700 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 = 4 years
So, we need to calculate the simple interest for the given time period, which is 4 years
Thus, Simple Interest for 4 years = 4 × Simple Interest for 1 year
= 4 × 2 = 8
Thus, simple interest for 4 years = 8
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 8 = 108
Calculation of the Principal
Now,
∵ If the Amount is 108, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/108
∴ If the Amount is 3996, then the Principal = 100/108 × 3996
= 100 × 3996/108
= 399600/108
= 3700
Thus, Principal = $3700
Thus, the sum borrowed = $3700 Answer
Similar Questions
(1) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 9% simple interest?
(2) Calculate the amount due if Linda borrowed a sum of $3350 at 4% simple interest for 3 years.
(3) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 8% simple interest?
(4) If Andrew paid $5568 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(5) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.
(6) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11946 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 8 years.
(8) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.
(9) If Mary borrowed $3050 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(10) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.