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) If Joshua paid $5880 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 7 years.
(3) What amount will be due after 2 years if John borrowed a sum of $3100 at a 5% simple interest?
(4) How much loan did Steven borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7590 to clear it?
(5) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 7 years.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 10% simple interest for 7 years.
(7) If Sandra paid $5340 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(8) How much loan did Kevin borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7810 to clear it?
(9) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 7% simple interest.
(10) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 4 years.