Question:
Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.
Correct Answer
$11400
Solution And Explanation
Solution
Given,
Principal (P) = $6000
Rate of Simple Interest (SI) = 9%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 10
= $6000 ×9/100 × 10
= 6000 × 9 × 10/100
= 54000 × 10/100
= 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) = 9%
And, Time (t) = 10 years
Thus, Amount (A)
= $6000 + ($6000 × 9% × 10)
= $6000 + ($6000 ×9/100 × 10)
= $6000 + (6000 × 9 × 10/100)
= $6000 + (54000 × 10/100)
= $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 = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $6000, the simple interest in 1 year
= 9/100 × 6000
= 9 × 6000/100
= 54000/100 = $540
Thus, simple interest for 1 year = $540
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $540 × 10 = $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) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.
(2) Charles had to pay $4485 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) If Paul paid $5076 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 9% simple interest?
(5) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 7 years.
(6) Find the amount to be paid if Charles borrowed a sum of $5900 at 8% simple interest for 7 years.
(7) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 3 years.
(8) What amount does John have to pay after 5 years if he takes a loan of $3200 at 10% simple interest?
(9) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 7 years.
(10) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 7% simple interest?