Question:
If Andrew paid $5760 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$4800
Solution And Explanation
Solution
Given,
Amount (A) = $5760
Rate of Simple Interest (R) = 5%
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
$5760 = P (1 + 5% × 4)
⇒ $5760 = P (1 + 5/100 × 4)
⇒ $5760 = P (1 + 5 × 4/100)
⇒ $5760 = P (1 + 20/100)
⇒ $5760 = P (100 + 20/100)
⇒ $5760 = P × 120/100
⇒ P × 120/100 = $5760
⇒ P = 5760/120/100
⇒ P = 5760 × 100/120
⇒ P = 5760 × 100/120
⇒ P = 576000/120
⇒ P = $4800
Thus, the sum borrowed (P) = $4800 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 = 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 × 5 = 20
Thus, simple interest for 4 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 5760, then the Principal = 100/120 × 5760
= 100 × 5760/120
= 576000/120
= 4800
Thus, Principal = $4800
Thus, the sum borrowed = $4800 Answer
Similar Questions
(1) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 4 years.
(2) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 3 years.
(3) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 3 years.
(4) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.
(5) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 3 years.
(7) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.
(8) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 8% simple interest?
(9) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 7% simple interest?
(10) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 4% simple interest?