Question:
Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.
Correct Answer
$10679
Solution And Explanation
Solution
Given,
Principal (P) = $5900
Rate of Simple Interest (SI) = 9%
Time (t) = 9 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) = $5900 × 9% × 9
= $5900 ×9/100 × 9
= 5900 × 9 × 9/100
= 53100 × 9/100
= 477900/100
= $4779
Thus, Simple Interest = $4779
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 = $5900 + $4779
= $10679
Thus, Amount to be paid = $10679 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 = $5900
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 9 years
Thus, Amount (A)
= $5900 + ($5900 × 9% × 9)
= $5900 + ($5900 ×9/100 × 9)
= $5900 + (5900 × 9 × 9/100)
= $5900 + (53100 × 9/100)
= $5900 + (477900/100)
= $5900 + $4779 = $10679
Thus, Amount (A) to be paid = $10679 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 $5900, the simple interest in 1 year
= 9/100 × 5900
= 9 × 5900/100
= 53100/100 = $531
Thus, simple interest for 1 year = $531
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $531 × 9 = $4779
Thus, Simple Interest (SI) = $4779
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5900 + $4779
= $10679
Thus, Amount to be paid = $10679 Answer
Similar Questions
(1) Kimberly had to pay $4929 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 8 years.
(3) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.
(4) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 4 years.
(6) How much loan did Michelle borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8687.5 to clear it?
(7) How much loan did Kevin borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8875 to clear it?
(8) If John paid $3840 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 5% simple interest?
(10) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 4 years.