Question:
If Steven paid $5520 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$4600
Solution And Explanation
Solution
Given,
Amount (A) = $5520
Rate of Simple Interest (R) = 5%
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
$5520 = P (1 + 5% × 4)
⇒ $5520 = P (1 + 5/100 × 4)
⇒ $5520 = P (1 + 5 × 4/100)
⇒ $5520 = P (1 + 20/100)
⇒ $5520 = P (100 + 20/100)
⇒ $5520 = P × 120/100
⇒ P × 120/100 = $5520
⇒ P = 5520/120/100
⇒ P = 5520 × 100/120
⇒ P = 5520 × 100/120
⇒ P = 552000/120
⇒ 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 = 5% per annum
Thus, Interest = 5% of principal
⇒ Interest = 5% of 100 = 5
Thus, Simple Interest for 1 year = 5
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 × 5 = 20
Thus, simple interest for 4 years = 20
Thus, Amount (A) = Principal + Interest
⇒ Amount = 100 + 20 = 120
Calculation of the Principal
Now,
∵ If the Amount is 120, then the Principal = 100
∴ If the Amount is 1, then the Principal = 100/120
∴ If the Amount is 5520, then the Principal = 100/120 × 5520
= 100 × 5520/120
= 552000/120
= 4600
Thus, Principal = $4600
Thus, the sum borrowed = $4600 Answer
Similar Questions
(1) How much loan did John borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6500 to clear it?
(2) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 10% simple interest?
(3) Calculate the amount due if Christopher borrowed a sum of $4000 at 5% simple interest for 3 years.
(4) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(5) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 10% simple interest?
(6) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 8% simple interest?
(7) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 4 years.
(8) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 6% simple interest?
(9) Sandra took a loan of $6900 at the rate of 10% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
(10) In how much time a principal of $3000 will amount to $3600 at a simple interest of 4% per annum?