Question:
Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.
Correct Answer
$9265
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 7%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 10
= $5450 ×7/100 × 10
= 5450 × 7 × 10/100
= 38150 × 10/100
= 381500/100
= $3815
Thus, Simple Interest = $3815
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 + $3815
= $9265
Thus, Amount to be paid = $9265 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) = 7%
And, Time (t) = 10 years
Thus, Amount (A)
= $5450 + ($5450 × 7% × 10)
= $5450 + ($5450 ×7/100 × 10)
= $5450 + (5450 × 7 × 10/100)
= $5450 + (38150 × 10/100)
= $5450 + (381500/100)
= $5450 + $3815 = $9265
Thus, Amount (A) to be paid = $9265 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5450, the simple interest in 1 year
= 7/100 × 5450
= 7 × 5450/100
= 38150/100 = $381.5
Thus, simple interest for 1 year = $381.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $381.5 × 10 = $3815
Thus, Simple Interest (SI) = $3815
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $3815
= $9265
Thus, Amount to be paid = $9265 Answer
Similar Questions
(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 7% simple interest for 3 years.
(2) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8869 to clear the loan, then find the time period of the loan.
(3) In how much time a principal of $3000 will amount to $3240 at a simple interest of 2% per annum?
(4) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 3 years.
(5) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.
(6) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 7 years.
(7) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.
(8) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 8 years.
(10) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 8 years.