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) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8050 to clear it?
(2) Mark had to pay $4928 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 7% simple interest?
(4) Calculate the amount due if David borrowed a sum of $3400 at 4% simple interest for 4 years.
(5) What amount does William have to pay after 6 years if he takes a loan of $3500 at 5% simple interest?
(6) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $7844 to clear the loan, then find the time period of the loan.
(7) What amount does John have to pay after 6 years if he takes a loan of $3200 at 3% simple interest?
(8) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 8% simple interest.
(9) In how much time a principal of $3100 will amount to $3348 at a simple interest of 2% per annum?
(10) If Donna paid $5238 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.