Question:
Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.
Correct Answer
$7820
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 4%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $5750 × 4% × 9
= $5750 ×4/100 × 9
= 5750 × 4 × 9/100
= 23000 × 9/100
= 207000/100
= $2070
Thus, Simple Interest = $2070
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 = $5750 + $2070
= $7820
Thus, Amount to be paid = $7820 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 = $5750
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 9 years
Thus, Amount (A)
= $5750 + ($5750 × 4% × 9)
= $5750 + ($5750 ×4/100 × 9)
= $5750 + (5750 × 4 × 9/100)
= $5750 + (23000 × 9/100)
= $5750 + (207000/100)
= $5750 + $2070 = $7820
Thus, Amount (A) to be paid = $7820 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5750, the simple interest in 1 year
= 4/100 × 5750
= 4 × 5750/100
= 23000/100 = $230
Thus, simple interest for 1 year = $230
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $230 × 9 = $2070
Thus, Simple Interest (SI) = $2070
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $2070
= $7820
Thus, Amount to be paid = $7820 Answer
Similar Questions
(1) Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 8 years.
(2) What amount will be due after 2 years if John borrowed a sum of $3100 at a 9% simple interest?
(3) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 9% simple interest.
(4) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.
(5) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.
(6) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 4% simple interest?
(7) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $8256 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 8 years.
(9) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 4 years.
(10) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.