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) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8140 to clear the loan, then find the time period of the loan.
(2) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $9088 to clear the loan, then find the time period of the loan.
(3) How much loan did Ronald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8625 to clear it?
(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.
(5) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.
(6) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 10% simple interest?
(7) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 8 years.
(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 8 years.
(9) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 4 years.
(10) If Barbara borrowed $3550 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.