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) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $9702 to clear the loan, then find the time period of the loan.
(2) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if John borrowed a sum of $3100 at a 4% simple interest?
(4) Thomas had to pay $4256 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) How much loan did David borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6480 to clear it?
(6) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $8946 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.
(8) In how much time a principal of $3200 will amount to $3680 at a simple interest of 3% per annum?
(9) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 8% simple interest?
(10) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.