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) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.
(2) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 2% simple interest?
(3) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.
(4) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 7% simple interest?
(5) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 3 years.
(6) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10988 to clear the loan, then find the time period of the loan.
(7) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 3% simple interest?
(8) Sandra had to pay $4984 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 will be due after 2 years if Joseph borrowed a sum of $3350 at a 6% simple interest?
(10) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 6% simple interest?