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) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 7 years.
(2) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 8% simple interest?
(3) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.
(4) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.
(5) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.
(6) If Joshua paid $5684 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11152 to clear the loan, then find the time period of the loan.
(8) Sarah took a loan of $5700 at the rate of 10% simple interest per annum. If he paid an amount of $9690 to clear the loan, then find the time period of the loan.
(9) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7560 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 7 years.