Question:
Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
Correct Answer
$9374
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 8%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 9
= $5450 ×8/100 × 9
= 5450 × 8 × 9/100
= 43600 × 9/100
= 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) = 8%
And, Time (t) = 9 years
Thus, Amount (A)
= $5450 + ($5450 × 8% × 9)
= $5450 + ($5450 ×8/100 × 9)
= $5450 + (5450 × 8 × 9/100)
= $5450 + (43600 × 9/100)
= $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 = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5450, the simple interest in 1 year
= 8/100 × 5450
= 8 × 5450/100
= 43600/100 = $436
Thus, simple interest for 1 year = $436
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $436 × 9 = $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) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $11008 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.
(3) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 3 years.
(4) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 8% simple interest?
(5) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 2% simple interest.
(6) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 7 years.
(7) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 2% simple interest.
(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 3 years.
(9) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(10) Find the amount to be paid if Linda borrowed a sum of $5350 at 6% simple interest for 7 years.