Question:
If Patricia paid $3654 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3150
Solution And Explanation
Solution
Given,
Amount (A) = $3654
Rate of Simple Interest (R) = 4%
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
$3654 = P (1 + 4% × 4)
⇒ $3654 = P (1 + 4/100 × 4)
⇒ $3654 = P (1 + 4 × 4/100)
⇒ $3654 = P (1 + 16/100)
⇒ $3654 = P (100 + 16/100)
⇒ $3654 = P × 116/100
⇒ P × 116/100 = $3654
⇒ P = 3654/116/100
⇒ P = 3654 × 100/116
⇒ P = 3654 × 100/116
⇒ P = 365400/116
⇒ 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 = 4% per annum
Thus, Interest = 4% of principal
⇒ Interest = 4% of 100 = 4
Thus, Simple Interest for 1 year = 4
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 × 4 = 16
Thus, simple interest for 4 years = 16
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 16 = 116
Calculation of the Principal
Now,
∵ If the Amount is 116, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/116
∴ If the Amount is 3654, then the Principal = 100/116 × 3654
= 100 × 3654/116
= 365400/116
= 3150
Thus, Principal = $3150
Thus, the sum borrowed = $3150 Answer
Similar Questions
(1) If Richard paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.
(3) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 6% simple interest?
(5) What amount does William have to pay after 5 years if he takes a loan of $3500 at 10% simple interest?
(6) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 10% simple interest?
(7) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8688 to clear the loan, then find the time period of the loan.
(8) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 7% simple interest?
(9) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 3 years.
(10) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 5% simple interest?