Question:
Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 8 years.
Correct Answer
$8050
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 5%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 8
= $5750 ×5/100 × 8
= 5750 × 5 × 8/100
= 28750 × 8/100
= 230000/100
= $2300
Thus, Simple Interest = $2300
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 + $2300
= $8050
Thus, Amount to be paid = $8050 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) = 5%
And, Time (t) = 8 years
Thus, Amount (A)
= $5750 + ($5750 × 5% × 8)
= $5750 + ($5750 ×5/100 × 8)
= $5750 + (5750 × 5 × 8/100)
= $5750 + (28750 × 8/100)
= $5750 + (230000/100)
= $5750 + $2300 = $8050
Thus, Amount (A) to be paid = $8050 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5750, the simple interest in 1 year
= 5/100 × 5750
= 5 × 5750/100
= 28750/100 = $287.5
Thus, simple interest for 1 year = $287.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $287.5 × 8 = $2300
Thus, Simple Interest (SI) = $2300
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $2300
= $8050
Thus, Amount to be paid = $8050 Answer
Similar Questions
(1) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 4 years.
(2) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11222 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 3 years.
(4) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10595 to clear the loan, then find the time period of the loan.
(5) If Jennifer borrowed $3250 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(6) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 5% simple interest.
(7) Calculate the amount due if Susan borrowed a sum of $3650 at 6% simple interest for 3 years.
(8) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 9% simple interest?
(9) Calculate the amount due if Mary borrowed a sum of $3050 at 6% simple interest for 4 years.
(10) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 10% simple interest?