Question:
If Michelle paid $5940 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$4950
Solution And Explanation
Solution
Given,
Amount (A) = $5940
Rate of Simple Interest (R) = 5%
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
$5940 = P (1 + 5% × 4)
⇒ $5940 = P (1 + 5/100 × 4)
⇒ $5940 = P (1 + 5 × 4/100)
⇒ $5940 = P (1 + 20/100)
⇒ $5940 = P (100 + 20/100)
⇒ $5940 = P × 120/100
⇒ P × 120/100 = $5940
⇒ P = 5940/120/100
⇒ P = 5940 × 100/120
⇒ P = 5940 × 100/120
⇒ P = 594000/120
⇒ P = $4950
Thus, the sum borrowed (P) = $4950 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 20
Thus, simple interest for 4 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 5940, then the Principal = 100/120 × 5940
= 100 × 5940/120
= 594000/120
= 4950
Thus, Principal = $4950
Thus, the sum borrowed = $4950 Answer
Similar Questions
(1) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 4% simple interest?
(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 8 years.
(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 7 years.
(4) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.
(5) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 4 years.
(7) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 9% simple interest.
(8) Patricia had to pay $3528 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) What amount does William have to pay after 5 years if he takes a loan of $3500 at 3% simple interest?
(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 3 years.