Question:
Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.
Correct Answer
$10407.5
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 9%
Time (t) = 9 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) = $5750 × 9% × 9
= $5750 ×9/100 × 9
= 5750 × 9 × 9/100
= 51750 × 9/100
= 465750/100
= $4657.5
Thus, Simple Interest = $4657.5
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 = $5750 + $4657.5
= $10407.5
Thus, Amount to be paid = $10407.5 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 = $5750
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 9 years
Thus, Amount (A)
= $5750 + ($5750 × 9% × 9)
= $5750 + ($5750 ×9/100 × 9)
= $5750 + (5750 × 9 × 9/100)
= $5750 + (51750 × 9/100)
= $5750 + (465750/100)
= $5750 + $4657.5 = $10407.5
Thus, Amount (A) to be paid = $10407.5 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 $5750, the simple interest in 1 year
= 9/100 × 5750
= 9 × 5750/100
= 51750/100 = $517.5
Thus, simple interest for 1 year = $517.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $517.5 × 9 = $4657.5
Thus, Simple Interest (SI) = $4657.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $4657.5
= $10407.5
Thus, Amount to be paid = $10407.5 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.
(2) Thomas took a loan of $5600 at the rate of 6% simple interest per annum. If he paid an amount of $8288 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if William borrowed a sum of $3500 at 6% simple interest for 4 years.
(4) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 7% simple interest.
(5) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 3% simple interest?
(6) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 10% simple interest for 7 years.
(8) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8804 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 5% simple interest.
(10) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.