Question:
If Jennifer paid $3770 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3250
Solution And Explanation
Solution
Given,
Amount (A) = $3770
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
$3770 = P (1 + 4% × 4)
⇒ $3770 = P (1 + 4/100 × 4)
⇒ $3770 = P (1 + 4 × 4/100)
⇒ $3770 = P (1 + 16/100)
⇒ $3770 = P (100 + 16/100)
⇒ $3770 = P × 116/100
⇒ P × 116/100 = $3770
⇒ P = 3770/116/100
⇒ P = 3770 × 100/116
⇒ P = 3770 × 100/116
⇒ P = 377000/116
⇒ P = $3250
Thus, the sum borrowed (P) = $3250 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 3770, then the Principal = 100/116 × 3770
= 100 × 3770/116
= 377000/116
= 3250
Thus, Principal = $3250
Thus, the sum borrowed = $3250 Answer
Similar Questions
(1) Calculate the amount due if Christopher borrowed a sum of $4000 at 8% simple interest for 3 years.
(2) What amount does David have to pay after 6 years if he takes a loan of $3400 at 10% simple interest?
(3) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 7% simple interest for 7 years.
(4) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 3 years.
(5) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 4 years.
(6) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 4 years.
(7) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.
(8) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.
(9) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 6% simple interest?
(10) If Emily paid $5510 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.