Question:
Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.
Correct Answer
$9683.5
Solution And Explanation
Solution
Given,
Principal (P) = $5350
Rate of Simple Interest (SI) = 9%
Time (t) = 9 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) = $5350 × 9% × 9
= $5350 ×9/100 × 9
= 5350 × 9 × 9/100
= 48150 × 9/100
= 433350/100
= $4333.5
Thus, Simple Interest = $4333.5
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 = $5350 + $4333.5
= $9683.5
Thus, Amount to be paid = $9683.5 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 = $5350
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 9 years
Thus, Amount (A)
= $5350 + ($5350 × 9% × 9)
= $5350 + ($5350 ×9/100 × 9)
= $5350 + (5350 × 9 × 9/100)
= $5350 + (48150 × 9/100)
= $5350 + (433350/100)
= $5350 + $4333.5 = $9683.5
Thus, Amount (A) to be paid = $9683.5 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 $5350, the simple interest in 1 year
= 9/100 × 5350
= 9 × 5350/100
= 48150/100 = $481.5
Thus, simple interest for 1 year = $481.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $481.5 × 9 = $4333.5
Thus, Simple Interest (SI) = $4333.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $4333.5
= $9683.5
Thus, Amount to be paid = $9683.5 Answer
Similar Questions
(1) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.
(2) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.
(4) Richard had to pay $3816 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6660 to clear the loan, then find the time period of the loan.
(6) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 3 years.
(8) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.
(9) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10540 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 9% simple interest?