Question:
Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 9% simple interest.
Correct Answer
$10136
Solution And Explanation
Solution
Given,
Principal (P) = $5600
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) = $5600 × 9% × 9
= $5600 ×9/100 × 9
= 5600 × 9 × 9/100
= 50400 × 9/100
= 453600/100
= $4536
Thus, Simple Interest = $4536
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 + $4536
= $10136
Thus, Amount to be paid = $10136 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) = 9 years
Thus, Amount (A)
= $5600 + ($5600 × 9% × 9)
= $5600 + ($5600 ×9/100 × 9)
= $5600 + (5600 × 9 × 9/100)
= $5600 + (50400 × 9/100)
= $5600 + (453600/100)
= $5600 + $4536 = $10136
Thus, Amount (A) to be paid = $10136 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 9 years
= Simple interest for 1 year × 9
= $504 × 9 = $4536
Thus, Simple Interest (SI) = $4536
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5600 + $4536
= $10136
Thus, Amount to be paid = $10136 Answer
Similar Questions
(1) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 7 years.
(2) Matthew had to pay $4452 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 7 years.
(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 7 years.
(5) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.
(6) If Patricia paid $3780 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 2% simple interest.
(8) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 7% simple interest.
(9) What amount will be due after 2 years if James borrowed a sum of $3000 at a 8% simple interest?
(10) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $6216 to clear the loan, then find the time period of the loan.