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) Michelle had to pay $5544 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
(3) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 4 years.
(4) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9288 to clear the loan, then find the time period of the loan.
(5) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 4% simple interest.
(7) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 2% simple interest?
(8) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 7% simple interest?
(9) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 2% simple interest?
(10) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 3 years.