Question:
If Joseph paid $4144 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$3700
Solution And Explanation
Solution
Given,
Amount (A) = $4144
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
$4144 = P (1 + 3% × 4)
⇒ $4144 = P (1 + 3/100 × 4)
⇒ $4144 = P (1 + 3 × 4/100)
⇒ $4144 = P (1 + 12/100)
⇒ $4144 = P (100 + 12/100)
⇒ $4144 = P × 112/100
⇒ P × 112/100 = $4144
⇒ P = 4144/112/100
⇒ P = 4144 × 100/112
⇒ P = 4144 × 100/112
⇒ P = 414400/112
⇒ P = $3700
Thus, the sum borrowed (P) = $3700 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 4144, then the Principal = 100/112 × 4144
= 100 × 4144/112
= 414400/112
= 3700
Thus, Principal = $3700
Thus, the sum borrowed = $3700 Answer
Similar Questions
(1) What amount does Patricia have to pay after 5 years if he takes a loan of $3150 at 5% simple interest?
(2) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 8 years.
(4) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.
(5) In how much time a principal of $3050 will amount to $3660 at a simple interest of 5% per annum?
(6) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 7 years.
(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 4% simple interest for 8 years.
(9) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 3 years.
(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 7 years.