Question:
Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.
Correct Answer
$10355
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 10%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 9
= $5450 ×10/100 × 9
= 5450 × 10 × 9/100
= 54500 × 9/100
= 490500/100
= $4905
Thus, Simple Interest = $4905
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 + $4905
= $10355
Thus, Amount to be paid = $10355 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) = 10%
And, Time (t) = 9 years
Thus, Amount (A)
= $5450 + ($5450 × 10% × 9)
= $5450 + ($5450 ×10/100 × 9)
= $5450 + (5450 × 10 × 9/100)
= $5450 + (54500 × 9/100)
= $5450 + (490500/100)
= $5450 + $4905 = $10355
Thus, Amount (A) to be paid = $10355 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5450, the simple interest in 1 year
= 10/100 × 5450
= 10 × 5450/100
= 54500/100 = $545
Thus, simple interest for 1 year = $545
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $545 × 9 = $4905
Thus, Simple Interest (SI) = $4905
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $4905
= $10355
Thus, Amount to be paid = $10355 Answer
Similar Questions
(1) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $7009 to clear the loan, then find the time period of the loan.
(2) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $9804 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 5% simple interest?
(4) What amount does William have to pay after 5 years if he takes a loan of $3500 at 10% simple interest?
(5) How much loan did Linda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5885 to clear it?
(6) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
(7) How much loan did Margaret borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7620 to clear it?
(8) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.
(9) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 10% 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.