Question:
Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 2% simple interest.
Correct Answer
$6900
Solution And Explanation
Solution
Given,
Principal (P) = $5750
Rate of Simple Interest (SI) = 2%
Time (t) = 10 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% × 10
= $5750 ×2/100 × 10
= 5750 × 2 × 10/100
= 11500 × 10/100
= 115000/100
= $1150
Thus, Simple Interest = $1150
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 + $1150
= $6900
Thus, Amount to be paid = $6900 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) = 10 years
Thus, Amount (A)
= $5750 + ($5750 × 2% × 10)
= $5750 + ($5750 ×2/100 × 10)
= $5750 + (5750 × 2 × 10/100)
= $5750 + (11500 × 10/100)
= $5750 + (115000/100)
= $5750 + $1150 = $6900
Thus, Amount (A) to be paid = $6900 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 10 years
= Simple interest for 1 year × 10
= $115 × 10 = $1150
Thus, Simple Interest (SI) = $1150
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5750 + $1150
= $6900
Thus, Amount to be paid = $6900 Answer
Similar Questions
(1) Joseph had to pay $3922 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Calculate the amount due if James borrowed a sum of $3000 at 7% simple interest for 4 years.
(3) How much loan did Laura borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9420 to clear it?
(4) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 8% simple interest for 4 years.
(5) How much loan did Mary borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $5807.5 to clear it?
(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 3% simple interest for 8 years.
(7) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 7 years.
(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 4 years.
(9) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8820 to clear the loan, then find the time period of the loan.
(10) Patricia had to pay $3339 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.