Question:
Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.
Correct Answer
$11400
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 10%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% per annum.
Method (1) Using Formula
Calculation of Simple Interest
Formula to Calculate Simple Interest
Simple Interest (SI) = Principal × Rate × Time
Thus, Simple Interest (SI) = $6000 × 10% × 9
= $6000 ×10/100 × 9
= 6000 × 10 × 9/100
= 60000 × 9/100
= 540000/100
= $5400
Thus, Simple Interest = $5400
Calculation of Amount
The total money paid to the lender by a borrower is called the Amount.
In other words, sum of priciple and interest is called the Amount.
Formula to Calculate the Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $5400
= $11400
Thus, Amount to be paid = $11400 Answer
Method (2)
Calculation of Amount when Principal, Rate of Simple Interest and Time are given
Calculation of Amount directly using Principal, SI, and Time
Formula to calculate the Amount
Amount (A) = Principal (P) + Principal(P) × Rate of Interest (SI) × Time (t)
⇒ A = P + PRT
Here in the question, P = $6000
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 9 years
Thus, Amount (A)
= $6000 + ($6000 × 10% × 9)
= $6000 + ($6000 ×10/100 × 9)
= $6000 + (6000 × 10 × 9/100)
= $6000 + (60000 × 9/100)
= $6000 + (540000/100)
= $6000 + $5400 = $11400
Thus, Amount (A) to be paid = $11400 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $6000, the simple interest in 1 year
= 10/100 × 6000
= 10 × 6000/100
= 60000/100 = $600
Thus, simple interest for 1 year = $600
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $600 × 9 = $5400
Thus, Simple Interest (SI) = $5400
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $6000 + $5400
= $11400
Thus, Amount to be paid = $11400 Answer
Similar Questions
(1) How much loan did Mark borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7360 to clear it?
(2) If Emily paid $5130 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5920 to clear the loan, then find the time period of the loan.
(4) If Lisa paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(6) Donna had to pay $5577.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) Find the amount to be paid if Karen borrowed a sum of $5950 at 10% simple interest for 7 years.
(8) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(9) In how much time a principal of $3050 will amount to $3416 at a simple interest of 3% per annum?
(10) If Emily paid $5700 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.