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) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 4 years.
(3) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 7 years.
(4) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 6% simple interest?
(5) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 7% simple interest?
(6) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 9% simple interest?
(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 9% simple interest?
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 7 years.
(9) How much loan did Ryan borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9085 to clear it?
(10) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 4 years.