Question:
Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.
Correct Answer
$10900
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 10%
Time (t) = 10 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% × 10
= $5450 ×10/100 × 10
= 5450 × 10 × 10/100
= 54500 × 10/100
= 545000/100
= $5450
Thus, Simple Interest = $5450
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 + $5450
= $10900
Thus, Amount to be paid = $10900 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) = 10 years
Thus, Amount (A)
= $5450 + ($5450 × 10% × 10)
= $5450 + ($5450 ×10/100 × 10)
= $5450 + (5450 × 10 × 10/100)
= $5450 + (54500 × 10/100)
= $5450 + (545000/100)
= $5450 + $5450 = $10900
Thus, Amount (A) to be paid = $10900 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 10 years
= Simple interest for 1 year × 10
= $545 × 10 = $5450
Thus, Simple Interest (SI) = $5450
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $5450
= $10900
Thus, Amount to be paid = $10900 Answer
Similar Questions
(1) Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 7 years.
(2) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 7 years.
(3) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.
(4) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $12060 to clear the loan, then find the time period of the loan.
(5) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $10660 to clear the loan, then find the time period of the loan.
(6) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.
(7) Anthony took a loan of $6600 at the rate of 8% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 4 years.
(9) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 4% simple interest?
(10) If Robert paid $3720 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.