Question:
If Andrew paid $5184 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$4800
Solution And Explanation
Solution
Given,
Amount (A) = $5184
Rate of Simple Interest (R) = 2%
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
$5184 = P (1 + 2% × 4)
⇒ $5184 = P (1 + 2/100 × 4)
⇒ $5184 = P (1 + 2 × 4/100)
⇒ $5184 = P (1 + 8/100)
⇒ $5184 = P (100 + 8/100)
⇒ $5184 = P × 108/100
⇒ P × 108/100 = $5184
⇒ P = 5184/108/100
⇒ P = 5184 × 100/108
⇒ P = 5184 × 100/108
⇒ P = 518400/108
⇒ P = $4800
Thus, the sum borrowed (P) = $4800 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 8
Thus, simple interest for 4 years = 8
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 8 = 108
Calculation of the Principal
Now,
∵ If the Amount is 108, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/108
∴ If the Amount is 5184, then the Principal = 100/108 × 5184
= 100 × 5184/108
= 518400/108
= 4800
Thus, Principal = $4800
Thus, the sum borrowed = $4800 Answer
Similar Questions
(1) In how much time a principal of $3050 will amount to $3416 at a simple interest of 3% per annum?
(2) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.
(3) What amount does William have to pay after 6 years if he takes a loan of $3500 at 5% simple interest?
(4) If Elizabeth borrowed $3450 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(5) How much loan did Christopher borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7200 to clear it?
(6) Calculate the amount due if Robert borrowed a sum of $3100 at 6% simple interest for 3 years.
(7) Michael had to pay $3498 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 7 years.
(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 8 years.
(10) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 4% simple interest?