Question:
If Karen paid $4740 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$3950
Solution And Explanation
Solution
Given,
Amount (A) = $4740
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
$4740 = P (1 + 5% × 4)
⇒ $4740 = P (1 + 5/100 × 4)
⇒ $4740 = P (1 + 5 × 4/100)
⇒ $4740 = P (1 + 20/100)
⇒ $4740 = P (100 + 20/100)
⇒ $4740 = P × 120/100
⇒ P × 120/100 = $4740
⇒ P = 4740/120/100
⇒ P = 4740 × 100/120
⇒ P = 4740 × 100/120
⇒ P = 474000/120
⇒ P = $3950
Thus, the sum borrowed (P) = $3950 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 4740, then the Principal = 100/120 × 4740
= 100 × 4740/120
= 474000/120
= 3950
Thus, Principal = $3950
Thus, the sum borrowed = $3950 Answer
Similar Questions
(1) Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 8 years.
(2) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 4% simple interest?
(3) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 7% simple interest?
(4) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6109 to clear the loan, then find the time period of the loan.
(5) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 2% simple interest?
(6) If Michelle paid $5940 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 3 years.
(8) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6808 to clear the loan, then find the time period of the loan.
(9) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 2% simple interest?
(10) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 6% simple interest?