Question:
Christopher had to pay $4480 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
$4000
Solution And Explanation
Solution
Given,
Amount (A) = $4480
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
$4480 = P (1 + 4% × 3)
⇒ $4480 = P (1 + 4/100 × 3)
⇒ $4480 = P (1 + 4 × 3/100)
⇒ $4480 = P (1 + 12/100)
⇒ $4480 = P (100 + 12/100)
⇒ $4480 = P × 112/100
⇒ P × 112/100 = $4480
⇒ P = 4480/112/100
⇒ P = 4480 × 100/112
⇒ P = 4480 × 100/112
⇒ P = 448000/112
⇒ P = $4000
Thus, the sum borrowed (P) = $4000 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 4480, then the Principal = 100/112 × 4480
= 100 × 4480/112
= 448000/112
= 4000
Thus, Principal = $4000
Thus, the sum borrowed = $4000 Answer
Similar Questions
(1) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 6% simple interest?
(2) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 10% simple interest?
(3) If Richard borrowed $3600 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 7 years.
(5) How much loan did Timothy borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9250 to clear it?
(6) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9834 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Linda borrowed a sum of $3350 at 5% simple interest for 4 years.
(8) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 7% simple interest?
(9) In how much time a principal of $3200 will amount to $3520 at a simple interest of 2% per annum?
(10) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.