Question:
Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 3 years.
Correct Answer
$3416
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (SI) = 4%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $3050 × 4% × 3
= $3050 ×4/100 × 3
= 3050 × 4 × 3/100
= 12200 × 3/100
= 36600/100
= $366
Thus, Simple Interest = $366
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 = $3050 + $366
= $3416
Thus, Amount to be paid = $3416 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 = $3050
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 3 years
Thus, Amount (A)
= $3050 + ($3050 × 4% × 3)
= $3050 + ($3050 ×4/100 × 3)
= $3050 + (3050 × 4 × 3/100)
= $3050 + (12200 × 3/100)
= $3050 + (36600/100)
= $3050 + $366 = $3416
Thus, Amount (A) to be paid = $3416 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $3050, the simple interest in 1 year
= 4/100 × 3050
= 4 × 3050/100
= 12200/100 = $122
Thus, simple interest for 1 year = $122
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $122 × 3 = $366
Thus, Simple Interest (SI) = $366
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3050 + $366
= $3416
Thus, Amount to be paid = $3416 Answer
Similar Questions
(1) Christopher had to pay $4600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(2) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11800 to clear the loan, then find the time period of the loan.
(3) If Lisa paid $4536 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 3 years.
(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 8 years.
(6) Anthony had to pay $4816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.
(8) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(9) Robert had to pay $3379 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 8 years.