Question:
If Karen paid $4424 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$3950
Solution And Explanation
Solution
Given,
Amount (A) = $4424
Rate of Simple Interest (R) = 3%
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
$4424 = P (1 + 3% × 4)
⇒ $4424 = P (1 + 3/100 × 4)
⇒ $4424 = P (1 + 3 × 4/100)
⇒ $4424 = P (1 + 12/100)
⇒ $4424 = P (100 + 12/100)
⇒ $4424 = P × 112/100
⇒ P × 112/100 = $4424
⇒ P = 4424/112/100
⇒ P = 4424 × 100/112
⇒ P = 4424 × 100/112
⇒ P = 442400/112
⇒ 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 12
Thus, simple interest for 4 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 4424, then the Principal = 100/112 × 4424
= 100 × 4424/112
= 442400/112
= 3950
Thus, Principal = $3950
Thus, the sum borrowed = $3950 Answer
Similar Questions
(1) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 7 years.
(2) How much loan did George borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9125 to clear it?
(3) Find the amount to be paid if David borrowed a sum of $5400 at 10% simple interest for 8 years.
(4) How much loan did Richard borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7000 to clear it?
(5) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?
(6) 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.
(7) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.
(8) If John paid $3584 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) Patricia had to pay $3622.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(10) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.