Question:
Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 9% simple interest.
Correct Answer
$10355
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 9%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 10
= $5450 ×9/100 × 10
= 5450 × 9 × 10/100
= 49050 × 10/100
= 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) = 9%
And, Time (t) = 10 years
Thus, Amount (A)
= $5450 + ($5450 × 9% × 10)
= $5450 + ($5450 ×9/100 × 10)
= $5450 + (5450 × 9 × 10/100)
= $5450 + (49050 × 10/100)
= $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 = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5450, the simple interest in 1 year
= 9/100 × 5450
= 9 × 5450/100
= 49050/100 = $490.5
Thus, simple interest for 1 year = $490.5
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $490.5 × 10 = $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) If Mary paid $3660 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.
(3) What amount does John have to pay after 5 years if he takes a loan of $3200 at 10% simple interest?
(4) If Susan paid $4380 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(5) Jennifer took a loan of $4500 at the rate of 9% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.
(6) Christopher had to pay $4600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 2% simple interest.
(8) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.
(9) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.
(10) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.