Question:
Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.
Correct Answer
$10640
Solution And Explanation
Solution
Given,
Principal (P) = $5600
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) = $5600 × 9% × 10
= $5600 ×9/100 × 10
= 5600 × 9 × 10/100
= 50400 × 10/100
= 504000/100
= $5040
Thus, Simple Interest = $5040
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 = $5600 + $5040
= $10640
Thus, Amount to be paid = $10640 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 = $5600
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 10 years
Thus, Amount (A)
= $5600 + ($5600 × 9% × 10)
= $5600 + ($5600 ×9/100 × 10)
= $5600 + (5600 × 9 × 10/100)
= $5600 + (50400 × 10/100)
= $5600 + (504000/100)
= $5600 + $5040 = $10640
Thus, Amount (A) to be paid = $10640 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 $5600, the simple interest in 1 year
= 9/100 × 5600
= 9 × 5600/100
= 50400/100 = $504
Thus, simple interest for 1 year = $504
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $504 × 10 = $5040
Thus, Simple Interest (SI) = $5040
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5600 + $5040
= $10640
Thus, Amount to be paid = $10640 Answer
Similar Questions
(1) If Mary paid $3538 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) If Andrew paid $5184 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.
(4) Daniel had to pay $4715 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.
(6) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 8% simple interest.
(8) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.
(10) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.