Question:
If Michael paid $3696 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$3300
Solution And Explanation
Solution
Given,
Amount (A) = $3696
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
$3696 = P (1 + 3% × 4)
⇒ $3696 = P (1 + 3/100 × 4)
⇒ $3696 = P (1 + 3 × 4/100)
⇒ $3696 = P (1 + 12/100)
⇒ $3696 = P (100 + 12/100)
⇒ $3696 = P × 112/100
⇒ P × 112/100 = $3696
⇒ P = 3696/112/100
⇒ P = 3696 × 100/112
⇒ P = 3696 × 100/112
⇒ P = 369600/112
⇒ P = $3300
Thus, the sum borrowed (P) = $3300 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 3696, then the Principal = 100/112 × 3696
= 100 × 3696/112
= 369600/112
= 3300
Thus, Principal = $3300
Thus, the sum borrowed = $3300 Answer
Similar Questions
(1) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 4% simple interest?
(2) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 9% simple interest for 4 years.
(4) In how much time a principal of $3100 will amount to $3379 at a simple interest of 3% per annum?
(5) What amount does James have to pay after 5 years if he takes a loan of $3000 at 7% simple interest?
(6) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.
(7) What amount does David have to pay after 6 years if he takes a loan of $3400 at 2% simple interest?
(8) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(9) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $10281 to clear the loan, then find the time period of the loan.
(10) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 2% simple interest?