Question:
Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 8 years.
Correct Answer
$10350
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 10%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 8
= $5750 ×10/100 × 8
= 5750 × 10 × 8/100
= 57500 × 8/100
= 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) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5750 + ($5750 × 10% × 8)
= $5750 + ($5750 ×10/100 × 8)
= $5750 + (5750 × 10 × 8/100)
= $5750 + (57500 × 8/100)
= $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 = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5750, the simple interest in 1 year
= 10/100 × 5750
= 10 × 5750/100
= 57500/100 = $575
Thus, simple interest for 1 year = $575
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $575 × 8 = $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 Michael have to pay after 5 years if he takes a loan of $3300 at 3% simple interest?
(2) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 4 years.
(4) Find the amount to be paid if William borrowed a sum of $5500 at 8% simple interest for 8 years.
(5) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.
(6) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9920 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Robert borrowed a sum of $5100 at 10% simple interest for 8 years.
(8) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 9% simple interest?
(9) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 3 years.
(10) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.