Question:
If Anthony paid $5160 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
Correct Answer
$4300
Solution And Explanation
Solution
Given,
Amount (A) = $5160
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
$5160 = P (1 + 5% × 4)
⇒ $5160 = P (1 + 5/100 × 4)
⇒ $5160 = P (1 + 5 × 4/100)
⇒ $5160 = P (1 + 20/100)
⇒ $5160 = P (100 + 20/100)
⇒ $5160 = P × 120/100
⇒ P × 120/100 = $5160
⇒ P = 5160/120/100
⇒ P = 5160 × 100/120
⇒ P = 5160 × 100/120
⇒ P = 516000/120
⇒ P = $4300
Thus, the sum borrowed (P) = $4300 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 5160, then the Principal = 100/120 × 5160
= 100 × 5160/120
= 516000/120
= 4300
Thus, Principal = $4300
Thus, the sum borrowed = $4300 Answer
Similar Questions
(1) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 8 years.
(2) What amount does David have to pay after 6 years if he takes a loan of $3400 at 7% simple interest?
(3) What amount does William have to pay after 6 years if he takes a loan of $3500 at 2% simple interest?
(4) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.
(5) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 5% simple interest.
(6) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $10296 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if David borrowed a sum of $3400 at 8% simple interest for 3 years.
(8) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 6% simple interest?
(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.
(10) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 4% simple interest?