Question:
Calculate the amount due if Patricia borrowed a sum of $3150 at 10% simple interest for 3 years.
Correct Answer
$4095
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 10%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 3
= $3150 ×10/100 × 3
= 3150 × 10 × 3/100
= 31500 × 3/100
= 94500/100
= $945
Thus, Simple Interest = $945
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 + $945
= $4095
Thus, Amount to be paid = $4095 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) = 10%
And, Time (t) = 3 years
Thus, Amount (A)
= $3150 + ($3150 × 10% × 3)
= $3150 + ($3150 ×10/100 × 3)
= $3150 + (3150 × 10 × 3/100)
= $3150 + (31500 × 3/100)
= $3150 + (94500/100)
= $3150 + $945 = $4095
Thus, Amount (A) to be paid = $4095 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3150, the simple interest in 1 year
= 10/100 × 3150
= 10 × 3150/100
= 31500/100 = $315
Thus, simple interest for 1 year = $315
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $315 × 3 = $945
Thus, Simple Interest (SI) = $945
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $945
= $4095
Thus, Amount to be paid = $4095 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.
(2) If Robert borrowed $3100 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 8 years.
(4) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 3 years.
(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 8 years.
(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 8 years.
(7) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 4 years.
(8) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $8976 to clear the loan, then find the time period of the loan.
(9) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 3 years.