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 Jessica borrowed a sum of $5750 at 7% simple interest for 8 years.
(2) Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 8 years.
(3) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.
(4) What amount does James have to pay after 6 years if he takes a loan of $3000 at 2% simple interest?
(5) How much loan did Sandra borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7417.5 to clear it?
(6) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 2% simple interest?
(7) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 10% simple interest?
(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 2% simple interest for 3 years.
(9) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $11247 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 4 years.