Question:
Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.
Correct Answer
$9864.5
Solution And Explanation
Solution
Given,
Principal (P) = $5450
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) = $5450 × 9% × 9
= $5450 ×9/100 × 9
= 5450 × 9 × 9/100
= 49050 × 9/100
= 441450/100
= $4414.5
Thus, Simple Interest = $4414.5
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 = $5450 + $4414.5
= $9864.5
Thus, Amount to be paid = $9864.5 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 = $5450
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 9 years
Thus, Amount (A)
= $5450 + ($5450 × 9% × 9)
= $5450 + ($5450 ×9/100 × 9)
= $5450 + (5450 × 9 × 9/100)
= $5450 + (49050 × 9/100)
= $5450 + (441450/100)
= $5450 + $4414.5 = $9864.5
Thus, Amount (A) to be paid = $9864.5 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 $5450, the simple interest in 1 year
= 9/100 × 5450
= 9 × 5450/100
= 49050/100 = $490.5
Thus, simple interest for 1 year = $490.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $490.5 × 9 = $4414.5
Thus, Simple Interest (SI) = $4414.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $4414.5
= $9864.5
Thus, Amount to be paid = $9864.5 Answer
Similar Questions
(1) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3000 will amount to $3600 at a simple interest of 5% per annum?
(3) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 3 years.
(4) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.
(5) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 7 years.
(7) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 7 years.
(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 2% simple interest for 3 years.
(9) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 4 years.
(10) Calculate the amount due if Susan borrowed a sum of $3650 at 2% simple interest for 3 years.