Question:
Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 8 years.
Correct Answer
$10234
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 9%
Time (t) = 8 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% × 8
= $5950 ×9/100 × 8
= 5950 × 9 × 8/100
= 53550 × 8/100
= 428400/100
= $4284
Thus, Simple Interest = $4284
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 + $4284
= $10234
Thus, Amount to be paid = $10234 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) = 8 years
Thus, Amount (A)
= $5950 + ($5950 × 9% × 8)
= $5950 + ($5950 ×9/100 × 8)
= $5950 + (5950 × 9 × 8/100)
= $5950 + (53550 × 8/100)
= $5950 + (428400/100)
= $5950 + $4284 = $10234
Thus, Amount (A) to be paid = $10234 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 8 years
= Simple interest for 1 year × 8
= $535.5 × 8 = $4284
Thus, Simple Interest (SI) = $4284
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $4284
= $10234
Thus, Amount to be paid = $10234 Answer
Similar Questions
(1) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(2) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.
(4) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 6% simple interest?
(5) Find the amount to be paid if Michael borrowed a sum of $5300 at 2% simple interest for 7 years.
(6) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7152 to clear the loan, then find the time period of the loan.
(7) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Thomas borrowed a sum of $3800 at 10% simple interest for 3 years.
(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 2% simple interest for 3 years.
(10) Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 8 years.