Question:
Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.
Correct Answer
$10355
Solution And Explanation
Solution
Given,
Principal (P) = $5450
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) = $5450 × 9% × 10
= $5450 ×9/100 × 10
= 5450 × 9 × 10/100
= 49050 × 10/100
= 490500/100
= $4905
Thus, Simple Interest = $4905
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 + $4905
= $10355
Thus, Amount to be paid = $10355 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) = 10 years
Thus, Amount (A)
= $5450 + ($5450 × 9% × 10)
= $5450 + ($5450 ×9/100 × 10)
= $5450 + (5450 × 9 × 10/100)
= $5450 + (49050 × 10/100)
= $5450 + (490500/100)
= $5450 + $4905 = $10355
Thus, Amount (A) to be paid = $10355 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 10 years
= Simple interest for 1 year × 10
= $490.5 × 10 = $4905
Thus, Simple Interest (SI) = $4905
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $4905
= $10355
Thus, Amount to be paid = $10355 Answer
Similar Questions
(1) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 3 years.
(2) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 4 years.
(3) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 8% simple interest?
(4) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(5) If Lisa paid $4374 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) If David borrowed $3400 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 3 years.
(8) Calculate the amount due if Michael borrowed a sum of $3300 at 3% simple interest for 3 years.
(9) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9020 to clear the loan, then find the time period of the loan.
(10) Kenneth had to pay $5750 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.