Question : If Kenneth paid $5600 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer $5000
Solution & Explanation
Solution
Given,
Amount (A) = $5600
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
$5600 = P (1 + 3% × 4)
⇒ $5600 = P (1 + 3/100 × 4)
⇒ $5600 = P (1 + 3 × 4/100)
⇒ $5600 = P (1 + 12/100)
⇒ $5600 = P (100 + 12/100)
⇒ $5600 = P × 112/100
⇒ P × 112/100 = $5600
⇒ P = 5600/112/100
⇒ P = 5600 × 100/112
⇒ P = 5600 × 100/112
⇒ P = 560000/112
⇒ P = $5000
Thus, the sum borrowed (P) = $5000 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 5600, then the Principal = 100/112 × 5600
= 100 × 5600/112
= 560000/112
= 5000
Thus, Principal = $5000
Thus, the sum borrowed = $5000 Answer
Similar Questions
(1) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 4% simple interest?
(3) Find the amount to be paid if Richard borrowed a sum of $5600 at 2% simple interest for 8 years.
(4) What amount will be due after 2 years if John borrowed a sum of $3100 at a 10% simple interest?
(5) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 6% simple interest?
(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 8 years.
(7) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 4 years.
(8) Find the amount to be paid if John borrowed a sum of $5200 at 9% simple interest for 8 years.
(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 8 years.