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) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 8 years.
(2) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 3% simple interest?
(3) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5440 to clear the loan, then find the time period of the loan.
(4) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.
(6) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?
(7) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.
(9) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10860 to clear the loan, then find the time period of the loan.
(10) Steven had to pay $5152 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.