Question:
Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 3 years.
Correct Answer
$3339
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 2%
Time (t) = 3 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) = $3150 × 2% × 3
= $3150 ×2/100 × 3
= 3150 × 2 × 3/100
= 6300 × 3/100
= 18900/100
= $189
Thus, Simple Interest = $189
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 = $3150 + $189
= $3339
Thus, Amount to be paid = $3339 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 = $3150
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 3 years
Thus, Amount (A)
= $3150 + ($3150 × 2% × 3)
= $3150 + ($3150 ×2/100 × 3)
= $3150 + (3150 × 2 × 3/100)
= $3150 + (6300 × 3/100)
= $3150 + (18900/100)
= $3150 + $189 = $3339
Thus, Amount (A) to be paid = $3339 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 $3150, the simple interest in 1 year
= 2/100 × 3150
= 2 × 3150/100
= 6300/100 = $63
Thus, simple interest for 1 year = $63
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $63 × 3 = $189
Thus, Simple Interest (SI) = $189
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $189
= $3339
Thus, Amount to be paid = $3339 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
(2) Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 8 years.
(3) Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 7 years.
(4) Find the amount to be paid if James borrowed a sum of $5000 at 9% simple interest for 8 years.
(5) How much loan did Thomas borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6670 to clear it?
(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 8 years.
(7) Calculate the amount due if Jessica borrowed a sum of $3750 at 10% simple interest for 3 years.
(8) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.
(9) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.