Question:
Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 7 years.
Correct Answer
$6594.5
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 3%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 7
= $5450 ×3/100 × 7
= 5450 × 3 × 7/100
= 16350 × 7/100
= 114450/100
= $1144.5
Thus, Simple Interest = $1144.5
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 + $1144.5
= $6594.5
Thus, Amount to be paid = $6594.5 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) = 3%
And, Time (t) = 7 years
Thus, Amount (A)
= $5450 + ($5450 × 3% × 7)
= $5450 + ($5450 ×3/100 × 7)
= $5450 + (5450 × 3 × 7/100)
= $5450 + (16350 × 7/100)
= $5450 + (114450/100)
= $5450 + $1144.5 = $6594.5
Thus, Amount (A) to be paid = $6594.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5450, the simple interest in 1 year
= 3/100 × 5450
= 3 × 5450/100
= 16350/100 = $163.5
Thus, simple interest for 1 year = $163.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $163.5 × 7 = $1144.5
Thus, Simple Interest (SI) = $1144.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $1144.5
= $6594.5
Thus, Amount to be paid = $6594.5 Answer
Similar Questions
(1) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 3 years.
(2) How much loan did Emily borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7425 to clear it?
(3) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.
(4) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 7 years.
(5) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 4% simple interest.
(6) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 8 years.
(7) Calculate the amount due if Mary borrowed a sum of $3050 at 3% simple interest for 3 years.
(8) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10136 to clear the loan, then find the time period of the loan.
(9) If Joshua paid $5684 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Calculate the amount due if Mary borrowed a sum of $3050 at 7% simple interest for 4 years.