Question:
Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.
Correct Answer
$10588.5
Solution And Explanation
Solution
Given,
Principal (P) = $5850
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) = $5850 × 9% × 9
= $5850 ×9/100 × 9
= 5850 × 9 × 9/100
= 52650 × 9/100
= 473850/100
= $4738.5
Thus, Simple Interest = $4738.5
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 = $5850 + $4738.5
= $10588.5
Thus, Amount to be paid = $10588.5 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 = $5850
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 9 years
Thus, Amount (A)
= $5850 + ($5850 × 9% × 9)
= $5850 + ($5850 ×9/100 × 9)
= $5850 + (5850 × 9 × 9/100)
= $5850 + (52650 × 9/100)
= $5850 + (473850/100)
= $5850 + $4738.5 = $10588.5
Thus, Amount (A) to be paid = $10588.5 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 $5850, the simple interest in 1 year
= 9/100 × 5850
= 9 × 5850/100
= 52650/100 = $526.5
Thus, simple interest for 1 year = $526.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $526.5 × 9 = $4738.5
Thus, Simple Interest (SI) = $4738.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5850 + $4738.5
= $10588.5
Thus, Amount to be paid = $10588.5 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.
(2) 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.
(3) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.
(4) 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?
(5) What amount does David have to pay after 6 years if he takes a loan of $3400 at 4% simple interest?
(6) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.
(7) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 3% simple interest.
(8) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 7% simple interest.
(9) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 3 years.
(10) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 10% simple interest?