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 Susan borrowed a sum of $3650 at 4% simple interest for 3 years.
(2) What amount does William have to pay after 5 years if he takes a loan of $3500 at 6% simple interest?
(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 7 years.
(4) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.
(5) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 7 years.
(7) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 3 years.
(8) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 5% simple interest?
(9) If James paid $3600 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) If Barbara paid $3976 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.