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) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(2) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7820 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 8 years.
(4) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 3 years.
(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 3 years.
(6) Find the amount to be paid if William borrowed a sum of $5500 at 7% simple interest for 8 years.
(7) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(8) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Susan borrowed a sum of $5650 at 10% simple interest for 7 years.
(10) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.