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) If Sandra paid $5162 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) Calculate the amount due if Jessica borrowed a sum of $3750 at 8% simple interest for 3 years.
(3) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 3 years.
(4) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8415 to clear it?
(5) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 6% simple interest?
(6) Mark had to pay $5060 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 8% simple interest?
(8) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 7% simple interest.
(9) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 4 years.
(10) Find the amount to be paid if William borrowed a sum of $5500 at 5% simple interest for 7 years.