Question:
If Steven paid $5152 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
Correct Answer
$4600
Solution And Explanation
Solution
Given,
Amount (A) = $5152
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
$5152 = P (1 + 3% × 4)
⇒ $5152 = P (1 + 3/100 × 4)
⇒ $5152 = P (1 + 3 × 4/100)
⇒ $5152 = P (1 + 12/100)
⇒ $5152 = P (100 + 12/100)
⇒ $5152 = P × 112/100
⇒ P × 112/100 = $5152
⇒ P = 5152/112/100
⇒ P = 5152 × 100/112
⇒ P = 5152 × 100/112
⇒ P = 515200/112
⇒ P = $4600
Thus, the sum borrowed (P) = $4600 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 5152, then the Principal = 100/112 × 5152
= 100 × 5152/112
= 515200/112
= 4600
Thus, Principal = $4600
Thus, the sum borrowed = $4600 Answer
Similar Questions
(1) If Charles borrowed $3900 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(2) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.
(3) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(4) Steven had to pay $5014 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 7 years.
(6) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 3 years.
(7) How much loan did Jason borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9625 to clear it?
(8) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(9) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7700 to clear it?
(10) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.