Question:
Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
Correct Answer
$10234
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 8%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 9
= $5950 ×8/100 × 9
= 5950 × 8 × 9/100
= 47600 × 9/100
= 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) = 8%
And, Time (t) = 9 years
Thus, Amount (A)
= $5950 + ($5950 × 8% × 9)
= $5950 + ($5950 ×8/100 × 9)
= $5950 + (5950 × 8 × 9/100)
= $5950 + (47600 × 9/100)
= $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 = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5950, the simple interest in 1 year
= 8/100 × 5950
= 8 × 5950/100
= 47600/100 = $476
Thus, simple interest for 1 year = $476
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $476 × 9 = $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) Find the amount to be paid if Thomas borrowed a sum of $5800 at 8% simple interest for 8 years.
(2) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 10% simple interest?
(3) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 7 years.
(4) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(5) In how much time a principal of $3050 will amount to $3294 at a simple interest of 2% per annum?
(6) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 4 years.
(7) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 3 years.
(8) Margaret took a loan of $6700 at the rate of 10% simple interest per annum. If he paid an amount of $10720 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 4% simple interest.
(10) If Ashley paid $5096 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.