Question:
Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 6% simple interest.
Correct Answer
$9200
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 6%
Time (t) = 10 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% × 10
= $5750 ×6/100 × 10
= 5750 × 6 × 10/100
= 34500 × 10/100
= 345000/100
= $3450
Thus, Simple Interest = $3450
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 + $3450
= $9200
Thus, Amount to be paid = $9200 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) = 10 years
Thus, Amount (A)
= $5750 + ($5750 × 6% × 10)
= $5750 + ($5750 ×6/100 × 10)
= $5750 + (5750 × 6 × 10/100)
= $5750 + (34500 × 10/100)
= $5750 + (345000/100)
= $5750 + $3450 = $9200
Thus, Amount (A) to be paid = $9200 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 10 years
= Simple interest for 1 year × 10
= $345 × 10 = $3450
Thus, Simple Interest (SI) = $3450
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $3450
= $9200
Thus, Amount to be paid = $9200 Answer
Similar Questions
(1) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 4 years.
(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 8 years.
(3) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8600 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 4 years.
(5) If Joshua paid $5488 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.
(7) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9617 to clear the loan, then find the time period of the loan.
(8) If Sandra paid $5340 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.
(10) If Christopher borrowed $4000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.