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) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 6% simple interest?
(2) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.
(4) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9180 to clear it?
(5) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.
(6) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 3 years.
(7) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 9% simple interest.
(8) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.
(9) How much loan did Carol borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7755 to clear it?
(10) How much loan did Charles borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6785 to clear it?