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) Find the amount to be paid if Susan borrowed a sum of $5650 at 5% simple interest for 7 years.
(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 4 years.
(3) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(4) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 4% simple interest?
(5) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 10% simple interest for 8 years.
(7) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.
(8) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7392 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if William borrowed a sum of $3250 at a 5% simple interest?
(10) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.