Question:
Kenneth had to pay $5600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
Correct Answer
$5000
Solution And Explanation
Solution
Given,
Amount (A) = $5600
Rate of Simple Interest (R) = 4%
Time (T) = 3 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 + 4% × 3)
⇒ $5600 = P (1 + 4/100 × 3)
⇒ $5600 = P (1 + 4 × 3/100)
⇒ $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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
Calculation of the Amount
Since, in the question, time = 3 years
So, we need to calculate the simple interest for the given time period, which is 3 years
Thus, Simple Interest for 3 years = 3 × Simple Interest for 1 year
= 3 × 4 = 12
Thus, simple interest for 3 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) How much loan did Paul borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7705 to clear it?
(2) In how much time a principal of $3100 will amount to $3410 at a simple interest of 5% per annum?
(3) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 3% simple interest?
(4) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 3 years.
(5) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 8 years.
(6) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 7% simple interest for 8 years.
(8) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 10% simple interest?
(9) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 10% simple interest?
(10) What amount does William have to pay after 5 years if he takes a loan of $3500 at 6% simple interest?