Question:
If Ashley paid $5460 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$4550
Solution And Explanation
Solution
Given,
Amount (A) = $5460
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
$5460 = P (1 + 5% × 4)
⇒ $5460 = P (1 + 5/100 × 4)
⇒ $5460 = P (1 + 5 × 4/100)
⇒ $5460 = P (1 + 20/100)
⇒ $5460 = P (100 + 20/100)
⇒ $5460 = P × 120/100
⇒ P × 120/100 = $5460
⇒ P = 5460/120/100
⇒ P = 5460 × 100/120
⇒ P = 5460 × 100/120
⇒ P = 546000/120
⇒ P = $4550
Thus, the sum borrowed (P) = $4550 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 5460, then the Principal = 100/120 × 5460
= 100 × 5460/120
= 546000/120
= 4550
Thus, Principal = $4550
Thus, the sum borrowed = $4550 Answer
Similar Questions
(1) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $9856 to clear the loan, then find the time period of the loan.
(2) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 9% simple interest?
(3) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.
(4) If Margaret paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 10% simple interest?
(6) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 4% simple interest.
(7) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 8 years.
(8) How much loan did David borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6210 to clear it?
(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 4 years.
(10) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.