Question:
Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.
Correct Answer
$10350
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 8%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 10
= $5750 ×8/100 × 10
= 5750 × 8 × 10/100
= 46000 × 10/100
= 460000/100
= $4600
Thus, Simple Interest = $4600
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 + $4600
= $10350
Thus, Amount to be paid = $10350 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) = 8%
And, Time (t) = 10 years
Thus, Amount (A)
= $5750 + ($5750 × 8% × 10)
= $5750 + ($5750 ×8/100 × 10)
= $5750 + (5750 × 8 × 10/100)
= $5750 + (46000 × 10/100)
= $5750 + (460000/100)
= $5750 + $4600 = $10350
Thus, Amount (A) to be paid = $10350 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5750, the simple interest in 1 year
= 8/100 × 5750
= 8 × 5750/100
= 46000/100 = $460
Thus, simple interest for 1 year = $460
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $460 × 10 = $4600
Thus, Simple Interest (SI) = $4600
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $4600
= $10350
Thus, Amount to be paid = $10350 Answer
Similar Questions
(1) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?
(2) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9760 to clear the loan, then find the time period of the loan.
(3) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6300 to clear it?
(4) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11600 to clear the loan, then find the time period of the loan.
(5) How much loan did John borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5980 to clear it?
(6) Calculate the amount due if James borrowed a sum of $3000 at 2% simple interest for 4 years.
(7) Calculate the amount due if Barbara borrowed a sum of $3550 at 7% simple interest for 3 years.
(8) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(9) If Linda borrowed $3350 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 4 years.