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) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 2% simple interest?
(2) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 3 years.
(3) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.
(4) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 7% simple interest?
(6) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 4% simple interest for 3 years.
(7) Matthew had to pay $4452 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 9% simple interest for 3 years.
(9) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 10% simple interest.
(10) If Richard paid $3888 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.