Question:
Calculate the amount due if Patricia borrowed a sum of $3150 at 9% simple interest for 3 years.
Correct Answer
$4000.5
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 9%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 3
= $3150 ×9/100 × 3
= 3150 × 9 × 3/100
= 28350 × 3/100
= 85050/100
= $850.5
Thus, Simple Interest = $850.5
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 + $850.5
= $4000.5
Thus, Amount to be paid = $4000.5 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) = 9%
And, Time (t) = 3 years
Thus, Amount (A)
= $3150 + ($3150 × 9% × 3)
= $3150 + ($3150 ×9/100 × 3)
= $3150 + (3150 × 9 × 3/100)
= $3150 + (28350 × 3/100)
= $3150 + (85050/100)
= $3150 + $850.5 = $4000.5
Thus, Amount (A) to be paid = $4000.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $3150, the simple interest in 1 year
= 9/100 × 3150
= 9 × 3150/100
= 28350/100 = $283.5
Thus, simple interest for 1 year = $283.5
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $283.5 × 3 = $850.5
Thus, Simple Interest (SI) = $850.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $850.5
= $4000.5
Thus, Amount to be paid = $4000.5 Answer
Similar Questions
(1) In how much time a principal of $3150 will amount to $3780 at a simple interest of 5% per annum?
(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 4 years.
(3) In how much time a principal of $3100 will amount to $3720 at a simple interest of 5% per annum?
(4) 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.
(5) If Christopher borrowed $4000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(6) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.
(7) If Charles paid $4212 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Joseph had to pay $4144 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) If Jennifer paid $3640 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 2% simple interest.