Question:
Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.
Correct Answer
$9231
Solution And Explanation
Solution
Given,
Principal (P) = $5100
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) = $5100 × 9% × 9
= $5100 ×9/100 × 9
= 5100 × 9 × 9/100
= 45900 × 9/100
= 413100/100
= $4131
Thus, Simple Interest = $4131
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 = $5100 + $4131
= $9231
Thus, Amount to be paid = $9231 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 = $5100
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 9 years
Thus, Amount (A)
= $5100 + ($5100 × 9% × 9)
= $5100 + ($5100 ×9/100 × 9)
= $5100 + (5100 × 9 × 9/100)
= $5100 + (45900 × 9/100)
= $5100 + (413100/100)
= $5100 + $4131 = $9231
Thus, Amount (A) to be paid = $9231 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 $5100, the simple interest in 1 year
= 9/100 × 5100
= 9 × 5100/100
= 45900/100 = $459
Thus, simple interest for 1 year = $459
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $459 × 9 = $4131
Thus, Simple Interest (SI) = $4131
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $4131
= $9231
Thus, Amount to be paid = $9231 Answer
Similar Questions
(1) If Andrew paid $5376 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(2) In how much time a principal of $3050 will amount to $3355 at a simple interest of 5% per annum?
(3) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.
(4) Michael had to pay $3795 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(5) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 7% simple interest?
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 8 years.
(7) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.
(8) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 8% simple interest?
(10) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7332 to clear the loan, then find the time period of the loan.