Question:
If Jessica paid $4350 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3750
Solution And Explanation
Solution
Given,
Amount (A) = $4350
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
$4350 = P (1 + 4% × 4)
⇒ $4350 = P (1 + 4/100 × 4)
⇒ $4350 = P (1 + 4 × 4/100)
⇒ $4350 = P (1 + 16/100)
⇒ $4350 = P (100 + 16/100)
⇒ $4350 = P × 116/100
⇒ P × 116/100 = $4350
⇒ P = 4350/116/100
⇒ P = 4350 × 100/116
⇒ P = 4350 × 100/116
⇒ P = 435000/116
⇒ P = $3750
Thus, the sum borrowed (P) = $3750 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 4350, then the Principal = 100/116 × 4350
= 100 × 4350/116
= 435000/116
= 3750
Thus, Principal = $3750
Thus, the sum borrowed = $3750 Answer
Similar Questions
(1) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 8% simple interest.
(2) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 5% simple interest.
(3) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 6% simple interest?
(4) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 3 years.
(5) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $8624 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.
(7) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 8 years.
(8) Michelle had to pay $5692.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 4 years.
(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 6% simple interest for 4 years.