Question:
Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 8 years.
Correct Answer
$9374
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 9%
Time (t) = 8 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% × 8
= $5450 ×9/100 × 8
= 5450 × 9 × 8/100
= 49050 × 8/100
= 392400/100
= $3924
Thus, Simple Interest = $3924
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 + $3924
= $9374
Thus, Amount to be paid = $9374 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) = 8 years
Thus, Amount (A)
= $5450 + ($5450 × 9% × 8)
= $5450 + ($5450 ×9/100 × 8)
= $5450 + (5450 × 9 × 8/100)
= $5450 + (49050 × 8/100)
= $5450 + (392400/100)
= $5450 + $3924 = $9374
Thus, Amount (A) to be paid = $9374 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 8 years
= Simple interest for 1 year × 8
= $490.5 × 8 = $3924
Thus, Simple Interest (SI) = $3924
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $3924
= $9374
Thus, Amount to be paid = $9374 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.
(2) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(3) Donna had to pay $5577.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) How much loan did Mary borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5807.5 to clear it?
(5) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 5% simple interest.
(6) How much loan did Matthew borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6820 to clear it?
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 8 years.
(8) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 8 years.
(9) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.
(10) If Steven paid $5152 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.