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) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 10% simple interest?
(2) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8470 to clear the loan, then find the time period of the loan.
(3) If Michael paid $3960 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(5) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.
(6) What amount does James have to pay after 5 years if he takes a loan of $3000 at 5% simple interest?
(7) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 10% simple interest.
(8) Margaret had to pay $4741.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.
(10) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.