Question:
If Michelle paid $5544 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$4950
Solution And Explanation
Solution
Given,
Amount (A) = $5544
Rate of Simple Interest (R) = 3%
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
$5544 = P (1 + 3% × 4)
⇒ $5544 = P (1 + 3/100 × 4)
⇒ $5544 = P (1 + 3 × 4/100)
⇒ $5544 = P (1 + 12/100)
⇒ $5544 = P (100 + 12/100)
⇒ $5544 = P × 112/100
⇒ P × 112/100 = $5544
⇒ P = 5544/112/100
⇒ P = 5544 × 100/112
⇒ P = 5544 × 100/112
⇒ P = 554400/112
⇒ 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 = 3% per annum
Thus, Interest = 3% of principal
⇒ Interest = 3% of 100 = 3
Thus, Simple Interest for 1 year = 3
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 × 3 = 12
Thus, simple interest for 4 years = 12
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 12 = 112
Calculation of the Principal
Now,
∵ If the Amount is 112, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/112
∴ If the Amount is 5544, then the Principal = 100/112 × 5544
= 100 × 5544/112
= 554400/112
= 4950
Thus, Principal = $4950
Thus, the sum borrowed = $4950 Answer
Similar Questions
(1) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.
(2) If Sarah borrowed $3850 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(3) How much loan did Lisa borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6957.5 to clear it?
(4) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8970 to clear it?
(5) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.
(6) Richard had to pay $4140 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 3 years.
(9) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 3% simple interest?
(10) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.