Question:
If Charles paid $4368 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$3900
Solution And Explanation
Solution
Given,
Amount (A) = $4368
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
$4368 = P (1 + 3% × 4)
⇒ $4368 = P (1 + 3/100 × 4)
⇒ $4368 = P (1 + 3 × 4/100)
⇒ $4368 = P (1 + 12/100)
⇒ $4368 = P (100 + 12/100)
⇒ $4368 = P × 112/100
⇒ P × 112/100 = $4368
⇒ P = 4368/112/100
⇒ P = 4368 × 100/112
⇒ P = 4368 × 100/112
⇒ P = 436800/112
⇒ P = $3900
Thus, the sum borrowed (P) = $3900 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 4368, then the Principal = 100/112 × 4368
= 100 × 4368/112
= 436800/112
= 3900
Thus, Principal = $3900
Thus, the sum borrowed = $3900 Answer
Similar Questions
(1) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 3 years.
(2) If Karen paid $4740 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(3) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.
(4) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 6% simple interest?
(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 7 years.
(6) Michael had to pay $3696 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.
(8) Robert had to pay $3472 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) If Karen paid $4582 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.