Question:
Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 8 years.
Correct Answer
$8510
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 6%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 8
= $5750 ×6/100 × 8
= 5750 × 6 × 8/100
= 34500 × 8/100
= 276000/100
= $2760
Thus, Simple Interest = $2760
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 + $2760
= $8510
Thus, Amount to be paid = $8510 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) = 6%
And, Time (t) = 8 years
Thus, Amount (A)
= $5750 + ($5750 × 6% × 8)
= $5750 + ($5750 ×6/100 × 8)
= $5750 + (5750 × 6 × 8/100)
= $5750 + (34500 × 8/100)
= $5750 + (276000/100)
= $5750 + $2760 = $8510
Thus, Amount (A) to be paid = $8510 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5750, the simple interest in 1 year
= 6/100 × 5750
= 6 × 5750/100
= 34500/100 = $345
Thus, simple interest for 1 year = $345
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $345 × 8 = $2760
Thus, Simple Interest (SI) = $2760
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $2760
= $8510
Thus, Amount to be paid = $8510 Answer
Similar Questions
(1) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.
(3) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7488 to clear the loan, then find the time period of the loan.
(4) If Margaret paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) What amount does David have to pay after 6 years if he takes a loan of $3400 at 6% simple interest?
(6) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 5% simple interest?
(7) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?
(8) Calculate the amount due if John borrowed a sum of $3200 at 7% simple interest for 4 years.
(9) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 3 years.
(10) In how much time a principal of $3000 will amount to $3600 at a simple interest of 4% per annum?