Question:
Find the amount to be paid if Jessica borrowed a sum of $5750 at 2% simple interest for 8 years.
Correct Answer
$6670
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 2%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 8
= $5750 ×2/100 × 8
= 5750 × 2 × 8/100
= 11500 × 8/100
= 92000/100
= $920
Thus, Simple Interest = $920
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 + $920
= $6670
Thus, Amount to be paid = $6670 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) = 2%
And, Time (t) = 8 years
Thus, Amount (A)
= $5750 + ($5750 × 2% × 8)
= $5750 + ($5750 ×2/100 × 8)
= $5750 + (5750 × 2 × 8/100)
= $5750 + (11500 × 8/100)
= $5750 + (92000/100)
= $5750 + $920 = $6670
Thus, Amount (A) to be paid = $6670 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5750, the simple interest in 1 year
= 2/100 × 5750
= 2 × 5750/100
= 11500/100 = $115
Thus, simple interest for 1 year = $115
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $115 × 8 = $920
Thus, Simple Interest (SI) = $920
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $920
= $6670
Thus, Amount to be paid = $6670 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.
(2) How much loan did Patricia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5665 to clear it?
(3) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
(5) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 10% simple interest?
(6) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $10030 to clear the loan, then find the time period of the loan.
(7) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 5% simple interest?
(8) If Barbara paid $3834 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.
(10) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 7 years.