Question:
Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 3 years.
Correct Answer
$3873.5
Solution And Explanation
Solution
Given,
Principal (P) = $3050
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) = $3050 × 9% × 3
= $3050 ×9/100 × 3
= 3050 × 9 × 3/100
= 27450 × 3/100
= 82350/100
= $823.5
Thus, Simple Interest = $823.5
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 = $3050 + $823.5
= $3873.5
Thus, Amount to be paid = $3873.5 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 = $3050
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 3 years
Thus, Amount (A)
= $3050 + ($3050 × 9% × 3)
= $3050 + ($3050 ×9/100 × 3)
= $3050 + (3050 × 9 × 3/100)
= $3050 + (27450 × 3/100)
= $3050 + (82350/100)
= $3050 + $823.5 = $3873.5
Thus, Amount (A) to be paid = $3873.5 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 $3050, the simple interest in 1 year
= 9/100 × 3050
= 9 × 3050/100
= 27450/100 = $274.5
Thus, simple interest for 1 year = $274.5
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $274.5 × 3 = $823.5
Thus, Simple Interest (SI) = $823.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3050 + $823.5
= $3873.5
Thus, Amount to be paid = $3873.5 Answer
Similar Questions
(1) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 7 years.
(2) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.
(3) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 4% simple interest?
(5) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 7 years.
(6) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(7) Charles had to pay $4134 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) Calculate the amount due after 10 years if John borrowed a sum of $5200 at a rate of 5% simple interest.
(9) If Susan paid $4234 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.