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) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9800 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 5% simple interest.
(3) How much loan did Donald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8125 to clear it?
(4) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 3 years.
(5) Karen had to pay $4187 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(7) 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.
(8) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $7546 to clear the loan, then find the time period of the loan.
(9) In how much time a principal of $3150 will amount to $3937.5 at a simple interest of 5% per annum?
(10) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.