Question:
Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.
Correct Answer
$10769.5
Solution And Explanation
Solution
Given,
Principal (P) = $5950
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) = $5950 × 9% × 9
= $5950 ×9/100 × 9
= 5950 × 9 × 9/100
= 53550 × 9/100
= 481950/100
= $4819.5
Thus, Simple Interest = $4819.5
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 = $5950 + $4819.5
= $10769.5
Thus, Amount to be paid = $10769.5 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 = $5950
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 9 years
Thus, Amount (A)
= $5950 + ($5950 × 9% × 9)
= $5950 + ($5950 ×9/100 × 9)
= $5950 + (5950 × 9 × 9/100)
= $5950 + (53550 × 9/100)
= $5950 + (481950/100)
= $5950 + $4819.5 = $10769.5
Thus, Amount (A) to be paid = $10769.5 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 $5950, the simple interest in 1 year
= 9/100 × 5950
= 9 × 5950/100
= 53550/100 = $535.5
Thus, simple interest for 1 year = $535.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $535.5 × 9 = $4819.5
Thus, Simple Interest (SI) = $4819.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $4819.5
= $10769.5
Thus, Amount to be paid = $10769.5 Answer
Similar Questions
(1) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 8% simple interest?
(2) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.
(3) Kenneth had to pay $5450 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.
(5) Kimberly had to pay $4929 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) If Jessica paid $4500 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(7) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 4% simple interest.
(8) Calculate the amount due if Mary borrowed a sum of $3050 at 8% simple interest for 3 years.
(9) If Anthony paid $5160 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.