Question:
Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 9% simple interest for 7 years.
Correct Answer
$8883.5
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 9%
Time (t) = 7 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% × 7
= $5450 ×9/100 × 7
= 5450 × 9 × 7/100
= 49050 × 7/100
= 343350/100
= $3433.5
Thus, Simple Interest = $3433.5
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 + $3433.5
= $8883.5
Thus, Amount to be paid = $8883.5 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) = 7 years
Thus, Amount (A)
= $5450 + ($5450 × 9% × 7)
= $5450 + ($5450 ×9/100 × 7)
= $5450 + (5450 × 9 × 7/100)
= $5450 + (49050 × 7/100)
= $5450 + (343350/100)
= $5450 + $3433.5 = $8883.5
Thus, Amount (A) to be paid = $8883.5 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 7 years
= Simple interest for 1 year × 7
= $490.5 × 7 = $3433.5
Thus, Simple Interest (SI) = $3433.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $3433.5
= $8883.5
Thus, Amount to be paid = $8883.5 Answer
Similar Questions
(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 7 years.
(2) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 3 years.
(4) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 7% simple interest?
(5) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.
(6) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $13200 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.
(8) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9184 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Linda borrowed a sum of $5350 at 9% simple interest for 8 years.
(10) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.