Question:
If Mark paid $4752 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
Correct Answer
$4400
Solution And Explanation
Solution
Given,
Amount (A) = $4752
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
$4752 = P (1 + 2% × 4)
⇒ $4752 = P (1 + 2/100 × 4)
⇒ $4752 = P (1 + 2 × 4/100)
⇒ $4752 = P (1 + 8/100)
⇒ $4752 = P (100 + 8/100)
⇒ $4752 = P × 108/100
⇒ P × 108/100 = $4752
⇒ P = 4752/108/100
⇒ P = 4752 × 100/108
⇒ P = 4752 × 100/108
⇒ P = 475200/108
⇒ P = $4400
Thus, the sum borrowed (P) = $4400 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 4752, then the Principal = 100/108 × 4752
= 100 × 4752/108
= 475200/108
= 4400
Thus, Principal = $4400
Thus, the sum borrowed = $4400 Answer
Similar Questions
(1) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10004 to clear the loan, then find the time period of the loan.
(2) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 8% simple interest?
(3) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 4 years.
(5) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.
(6) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 8% simple interest?
(7) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.
(8) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 3% simple interest?
(9) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.
(10) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 7% simple interest?