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 Thomas borrowed a sum of $5800 at 2% simple interest for 8 years.
(2) If Charles borrowed $3900 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(3) Calculate the amount due if Karen borrowed a sum of $3950 at 9% simple interest for 4 years.
(4) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 4% simple interest?
(6) What amount will be due after 2 years if David borrowed a sum of $3200 at a 4% simple interest?
(7) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6556 to clear the loan, then find the time period of the loan.
(8) Sarah had to pay $4081 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) If Christopher borrowed $4000 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 10% simple interest?