Question:
If Nancy paid $4814 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$4150
Solution And Explanation
Solution
Given,
Amount (A) = $4814
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
$4814 = P (1 + 4% × 4)
⇒ $4814 = P (1 + 4/100 × 4)
⇒ $4814 = P (1 + 4 × 4/100)
⇒ $4814 = P (1 + 16/100)
⇒ $4814 = P (100 + 16/100)
⇒ $4814 = P × 116/100
⇒ P × 116/100 = $4814
⇒ P = 4814/116/100
⇒ P = 4814 × 100/116
⇒ P = 4814 × 100/116
⇒ P = 481400/116
⇒ P = $4150
Thus, the sum borrowed (P) = $4150 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 4814, then the Principal = 100/116 × 4814
= 100 × 4814/116
= 481400/116
= 4150
Thus, Principal = $4150
Thus, the sum borrowed = $4150 Answer
Similar Questions
(1) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 4 years.
(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 7 years.
(3) If Elizabeth paid $3864 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 5% simple interest?
(5) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7335 to clear the loan, then find the time period of the loan.
(6) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.
(8) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.
(9) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% simple interest for 8 years.
(10) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 3% simple interest?