Question:
If Donald paid $4860 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$4500
Solution And Explanation
Solution
Given,
Amount (A) = $4860
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
$4860 = P (1 + 2% × 4)
⇒ $4860 = P (1 + 2/100 × 4)
⇒ $4860 = P (1 + 2 × 4/100)
⇒ $4860 = P (1 + 8/100)
⇒ $4860 = P (100 + 8/100)
⇒ $4860 = P × 108/100
⇒ P × 108/100 = $4860
⇒ P = 4860/108/100
⇒ P = 4860 × 100/108
⇒ P = 4860 × 100/108
⇒ P = 486000/108
⇒ P = $4500
Thus, the sum borrowed (P) = $4500 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 4860, then the Principal = 100/108 × 4860
= 100 × 4860/108
= 486000/108
= 4500
Thus, Principal = $4500
Thus, the sum borrowed = $4500 Answer
Similar Questions
(1) In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?
(2) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 3 years.
(3) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 3% simple interest?
(4) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 8% simple interest?
(5) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 8% simple interest?
(6) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 6% simple interest?
(7) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8700 to clear it?
(8) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 3 years.
(9) If Thomas paid $4408 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 4 years.