Question:
If Lisa paid $4374 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$4050
Solution And Explanation
Solution
Given,
Amount (A) = $4374
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
$4374 = P (1 + 2% × 4)
⇒ $4374 = P (1 + 2/100 × 4)
⇒ $4374 = P (1 + 2 × 4/100)
⇒ $4374 = P (1 + 8/100)
⇒ $4374 = P (100 + 8/100)
⇒ $4374 = P × 108/100
⇒ P × 108/100 = $4374
⇒ P = 4374/108/100
⇒ P = 4374 × 100/108
⇒ P = 4374 × 100/108
⇒ P = 437400/108
⇒ P = $4050
Thus, the sum borrowed (P) = $4050 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 4374, then the Principal = 100/108 × 4374
= 100 × 4374/108
= 437400/108
= 4050
Thus, Principal = $4050
Thus, the sum borrowed = $4050 Answer
Similar Questions
(1) Calculate the amount due if Charles borrowed a sum of $3900 at 8% simple interest for 3 years.
(2) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 3 years.
(3) Calculate the amount due if John borrowed a sum of $3200 at 5% simple interest for 3 years.
(4) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.
(5) How much loan did Margaret borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6985 to clear it?
(6) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 3 years.
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 7 years.
(8) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 7% simple interest for 4 years.
(9) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 2% simple interest?
(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 7 years.