Question:
Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.
Correct Answer
$8050
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 4%
Time (t) = 10 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% × 10
= $5750 ×4/100 × 10
= 5750 × 4 × 10/100
= 23000 × 10/100
= 230000/100
= $2300
Thus, Simple Interest = $2300
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 + $2300
= $8050
Thus, Amount to be paid = $8050 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) = 10 years
Thus, Amount (A)
= $5750 + ($5750 × 4% × 10)
= $5750 + ($5750 ×4/100 × 10)
= $5750 + (5750 × 4 × 10/100)
= $5750 + (23000 × 10/100)
= $5750 + (230000/100)
= $5750 + $2300 = $8050
Thus, Amount (A) to be paid = $8050 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 10 years
= Simple interest for 1 year × 10
= $230 × 10 = $2300
Thus, Simple Interest (SI) = $2300
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $2300
= $8050
Thus, Amount to be paid = $8050 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 9% simple interest.
(2) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 2% simple interest?
(3) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 10% simple interest.
(4) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $9548 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 7 years.
(6) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 7% simple interest?
(7) How much loan did Sandra borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7740 to clear it?
(8) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 8% simple interest?
(9) Find the amount to be paid if Richard borrowed a sum of $5600 at 10% simple interest for 7 years.
(10) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.