Question:
If Patricia paid $3402 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$3150
Solution And Explanation
Solution
Given,
Amount (A) = $3402
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
$3402 = P (1 + 2% × 4)
⇒ $3402 = P (1 + 2/100 × 4)
⇒ $3402 = P (1 + 2 × 4/100)
⇒ $3402 = P (1 + 8/100)
⇒ $3402 = P (100 + 8/100)
⇒ $3402 = P × 108/100
⇒ P × 108/100 = $3402
⇒ P = 3402/108/100
⇒ P = 3402 × 100/108
⇒ P = 3402 × 100/108
⇒ P = 340200/108
⇒ P = $3150
Thus, the sum borrowed (P) = $3150 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 3402, then the Principal = 100/108 × 3402
= 100 × 3402/108
= 340200/108
= 3150
Thus, Principal = $3150
Thus, the sum borrowed = $3150 Answer
Similar Questions
(1) Calculate the amount due if Robert borrowed a sum of $3100 at 6% simple interest for 4 years.
(2) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 4% simple interest?
(3) Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 4 years.
(4) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 10% simple interest?
(5) If Andrew paid $5760 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 4% simple interest?
(7) How much loan did Matthew borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7130 to clear it?
(8) Find the amount to be paid if John borrowed a sum of $5200 at 3% simple interest for 7 years.
(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 8 years.
(10) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.