Question:
If Thomas paid $4408 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
Correct Answer
$3800
Solution And Explanation
Solution
Given,
Amount (A) = $4408
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
$4408 = P (1 + 4% × 4)
⇒ $4408 = P (1 + 4/100 × 4)
⇒ $4408 = P (1 + 4 × 4/100)
⇒ $4408 = P (1 + 16/100)
⇒ $4408 = P (100 + 16/100)
⇒ $4408 = P × 116/100
⇒ P × 116/100 = $4408
⇒ P = 4408/116/100
⇒ P = 4408 × 100/116
⇒ P = 4408 × 100/116
⇒ P = 440800/116
⇒ P = $3800
Thus, the sum borrowed (P) = $3800 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 4408, then the Principal = 100/116 × 4408
= 100 × 4408/116
= 440800/116
= 3800
Thus, Principal = $3800
Thus, the sum borrowed = $3800 Answer
Similar Questions
(1) If Karen borrowed $3950 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(2) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 7% simple interest?
(3) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.
(4) What amount does Joseph have to pay after 6 years if he takes a loan of $3700 at 2% simple interest?
(5) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.
(6) If Matthew paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 8% simple interest.
(8) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.
(9) Joshua had to pay $5341 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 7 years.