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) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7335 to clear the loan, then find the time period of the loan.
(2) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 3% simple interest?
(3) If David paid $4080 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 7% simple interest?
(5) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 5% simple interest.
(6) If John paid $3584 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 5% simple interest?
(8) How much loan did Thomas borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6670 to clear it?
(9) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 7% simple interest?
(10) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 9% simple interest.