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) Calculate the amount due if Jennifer borrowed a sum of $3250 at 9% simple interest for 4 years.
(2) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9800 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.
(4) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $5960 to clear the loan, then find the time period of the loan.
(5) If Michael borrowed $3300 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(6) How much loan did Joshua borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7590 to clear it?
(7) How much loan did Emily borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8100 to clear it?
(8) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 5% simple interest?
(9) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Charles borrowed a sum of $3900 at 6% simple interest for 4 years.