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) James took a loan of $4000 at the rate of 8% simple interest per annum. If he paid an amount of $6240 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 7 years.
(3) How much loan did Ronald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8625 to clear it?
(4) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 10% simple interest?
(6) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 6% simple interest?
(7) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.
(8) Calculate the amount due if Susan borrowed a sum of $3650 at 9% simple interest for 4 years.
(9) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $6958 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 3% simple interest.