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 if Patricia borrowed a sum of $3150 at 6% simple interest for 4 years.
(2) How much loan did Lisa borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6655 to clear it?
(3) How much loan did Carol borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8460 to clear it?
(4) If Michelle paid $5940 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 10% simple interest?
(6) If Donald paid $5220 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 3 years.
(8) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 3 years.
(10) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.