Question:
Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
Correct Answer
$9810
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 8%
Time (t) = 10 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% × 10
= $5450 ×8/100 × 10
= 5450 × 8 × 10/100
= 43600 × 10/100
= 436000/100
= $4360
Thus, Simple Interest = $4360
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 + $4360
= $9810
Thus, Amount to be paid = $9810 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) = 10 years
Thus, Amount (A)
= $5450 + ($5450 × 8% × 10)
= $5450 + ($5450 ×8/100 × 10)
= $5450 + (5450 × 8 × 10/100)
= $5450 + (43600 × 10/100)
= $5450 + (436000/100)
= $5450 + $4360 = $9810
Thus, Amount (A) to be paid = $9810 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 10 years
= Simple interest for 1 year × 10
= $436 × 10 = $4360
Thus, Simple Interest (SI) = $4360
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $4360
= $9810
Thus, Amount to be paid = $9810 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 6% simple interest.
(2) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 7 years.
(4) 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.
(5) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 7 years.
(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 7 years.
(7) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 3 years.
(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 3 years.
(9) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 3 years.
(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 8 years.