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 if Charles borrowed a sum of $3900 at 3% simple interest for 4 years.
(2) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 7 years.
(3) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.
(5) Calculate the amount due if Jessica borrowed a sum of $3750 at 9% simple interest for 3 years.
(6) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 10% simple interest?
(7) Calculate the amount due if James borrowed a sum of $3000 at 10% simple interest for 4 years.
(8) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 2% simple interest.
(9) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $13300 to clear the loan, then find the time period of the loan.
(10) If Jennifer paid $3770 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.