Question:
Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.
Correct Answer
$11305
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 9%
Time (t) = 10 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% × 10
= $5950 ×9/100 × 10
= 5950 × 9 × 10/100
= 53550 × 10/100
= 535500/100
= $5355
Thus, Simple Interest = $5355
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 + $5355
= $11305
Thus, Amount to be paid = $11305 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) = 10 years
Thus, Amount (A)
= $5950 + ($5950 × 9% × 10)
= $5950 + ($5950 ×9/100 × 10)
= $5950 + (5950 × 9 × 10/100)
= $5950 + (53550 × 10/100)
= $5950 + (535500/100)
= $5950 + $5355 = $11305
Thus, Amount (A) to be paid = $11305 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 10 years
= Simple interest for 1 year × 10
= $535.5 × 10 = $5355
Thus, Simple Interest (SI) = $5355
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $5355
= $11305
Thus, Amount to be paid = $11305 Answer
Similar Questions
(1) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 4 years.
(3) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?
(4) 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.
(5) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 9% simple interest?
(6) Jennifer had to pay $3737.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 6% simple interest?
(8) Michelle had to pay $5692.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 4% simple interest?
(10) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7748 to clear the loan, then find the time period of the loan.