Question:
If Michelle paid $5742 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$4950
Solution And Explanation
Solution
Given,
Amount (A) = $5742
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
$5742 = P (1 + 4% × 4)
⇒ $5742 = P (1 + 4/100 × 4)
⇒ $5742 = P (1 + 4 × 4/100)
⇒ $5742 = P (1 + 16/100)
⇒ $5742 = P (100 + 16/100)
⇒ $5742 = P × 116/100
⇒ P × 116/100 = $5742
⇒ P = 5742/116/100
⇒ P = 5742 × 100/116
⇒ P = 5742 × 100/116
⇒ P = 574200/116
⇒ 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 = 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 5742, then the Principal = 100/116 × 5742
= 100 × 5742/116
= 574200/116
= 4950
Thus, Principal = $4950
Thus, the sum borrowed = $4950 Answer
Similar Questions
(1) What amount does William have to pay after 6 years if he takes a loan of $3500 at 2% simple interest?
(2) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 9% simple interest?
(3) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.
(4) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 4 years.
(5) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $8736 to clear the loan, then find the time period of the loan.
(6) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.
(7) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 7 years.
(9) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 3 years.
(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 8 years.