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) How much loan did Michael borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6095 to clear it?
(2) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 7% simple interest?
(3) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(4) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
(6) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 3 years.
(8) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 4 years.
(9) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?
(10) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 4% simple interest?