Question:
If Robert paid $3596 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3100
Solution And Explanation
Solution
Given,
Amount (A) = $3596
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
$3596 = P (1 + 4% × 4)
⇒ $3596 = P (1 + 4/100 × 4)
⇒ $3596 = P (1 + 4 × 4/100)
⇒ $3596 = P (1 + 16/100)
⇒ $3596 = P (100 + 16/100)
⇒ $3596 = P × 116/100
⇒ P × 116/100 = $3596
⇒ P = 3596/116/100
⇒ P = 3596 × 100/116
⇒ P = 3596 × 100/116
⇒ P = 359600/116
⇒ P = $3100
Thus, the sum borrowed (P) = $3100 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 3596, then the Principal = 100/116 × 3596
= 100 × 3596/116
= 359600/116
= 3100
Thus, Principal = $3100
Thus, the sum borrowed = $3100 Answer
Similar Questions
(1) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.
(3) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 2% simple interest?
(4) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 5% simple interest?
(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 8 years.
(6) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 4 years.
(7) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 7% simple interest?
(8) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 8% simple interest?
(9) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 7 years.
(10) What amount does William have to pay after 6 years if he takes a loan of $3500 at 8% simple interest?