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) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 9% simple interest?
(2) Calculate the amount due if John borrowed a sum of $3200 at 2% simple interest for 4 years.
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 3% simple interest for 4 years.
(4) If Jessica paid $4050 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 7 years.
(6) What amount will be due after 2 years if William borrowed a sum of $3250 at a 9% simple interest?
(7) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 9% simple interest.
(8) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 8% simple interest?
(9) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 9% simple interest?
(10) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7740 to clear the loan, then find the time period of the loan.