Question:
Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 5% simple interest.
Correct Answer
$8175
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 5%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 10
= $5450 ×5/100 × 10
= 5450 × 5 × 10/100
= 27250 × 10/100
= 272500/100
= $2725
Thus, Simple Interest = $2725
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 + $2725
= $8175
Thus, Amount to be paid = $8175 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) = 5%
And, Time (t) = 10 years
Thus, Amount (A)
= $5450 + ($5450 × 5% × 10)
= $5450 + ($5450 ×5/100 × 10)
= $5450 + (5450 × 5 × 10/100)
= $5450 + (27250 × 10/100)
= $5450 + (272500/100)
= $5450 + $2725 = $8175
Thus, Amount (A) to be paid = $8175 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5450, the simple interest in 1 year
= 5/100 × 5450
= 5 × 5450/100
= 27250/100 = $272.5
Thus, simple interest for 1 year = $272.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $272.5 × 10 = $2725
Thus, Simple Interest (SI) = $2725
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $2725
= $8175
Thus, Amount to be paid = $8175 Answer
Similar Questions
(1) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
(2) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.
(3) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?
(4) Michael had to pay $3696 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $8550 to clear the loan, then find the time period of the loan.
(6) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.
(8) Sandra had to pay $4850.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Calculate the amount due if James borrowed a sum of $3000 at 8% simple interest for 4 years.
(10) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7602 to clear the loan, then find the time period of the loan.