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) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?
(2) In how much time a principal of $3100 will amount to $3472 at a simple interest of 3% per annum?
(3) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 4 years.
(5) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 5% simple interest.
(6) If Thomas borrowed $3800 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6106 to clear the loan, then find the time period of the loan.
(8) Margaret had to pay $4872 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $6674 to clear the loan, then find the time period of the loan.
(10) If William borrowed $3500 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.