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) John had to pay $3584 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 3% simple interest for 7 years.
(3) In how much time a principal of $3100 will amount to $3410 at a simple interest of 2% per annum?
(4) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.
(5) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 10% simple interest?
(6) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 8 years.
(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 7 years.
(9) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 5% simple interest?