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) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(2) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.
(3) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6037.5 to clear it?
(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 5% simple interest for 3 years.
(5) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 6% simple interest?
(6) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 7% simple interest.
(7) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if David borrowed a sum of $3200 at a 9% simple interest?
(9) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 9% simple interest?
(10) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8930 to clear the loan, then find the time period of the loan.