Question:
If Daniel paid $4428 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$4100
Solution And Explanation
Solution
Given,
Amount (A) = $4428
Rate of Simple Interest (R) = 2%
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
$4428 = P (1 + 2% × 4)
⇒ $4428 = P (1 + 2/100 × 4)
⇒ $4428 = P (1 + 2 × 4/100)
⇒ $4428 = P (1 + 8/100)
⇒ $4428 = P (100 + 8/100)
⇒ $4428 = P × 108/100
⇒ P × 108/100 = $4428
⇒ P = 4428/108/100
⇒ P = 4428 × 100/108
⇒ P = 4428 × 100/108
⇒ P = 442800/108
⇒ P = $4100
Thus, the sum borrowed (P) = $4100 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 = 2% per annum
Thus, Interest = 2% of principal
⇒ Interest = 2% of 100 = 2
Thus, Simple Interest for 1 year = 2
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 × 2 = 8
Thus, simple interest for 4 years = 8
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 8 = 108
Calculation of the Principal
Now,
∵ If the Amount is 108, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/108
∴ If the Amount is 4428, then the Principal = 100/108 × 4428
= 100 × 4428/108
= 442800/108
= 4100
Thus, Principal = $4100
Thus, the sum borrowed = $4100 Answer
Similar Questions
(1) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 8 years.
(2) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 7 years.
(4) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 3 years.
(5) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 5% simple interest?
(6) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.
(7) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 4 years.
(8) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 4% simple interest for 3 years.
(10) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.