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) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
(2) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.
(3) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(4) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 8% simple interest?
(5) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $8400 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if James borrowed a sum of $3000 at a 6% simple interest?
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 7 years.
(8) How much loan did Michelle borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8340 to clear it?
(9) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 5% simple interest?
(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 7 years.