Question:
Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 10% simple interest.
Correct Answer
$11305
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 10%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 9
= $5950 ×10/100 × 9
= 5950 × 10 × 9/100
= 59500 × 9/100
= 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) = 10%
And, Time (t) = 9 years
Thus, Amount (A)
= $5950 + ($5950 × 10% × 9)
= $5950 + ($5950 ×10/100 × 9)
= $5950 + (5950 × 10 × 9/100)
= $5950 + (59500 × 9/100)
= $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 = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5950, the simple interest in 1 year
= 10/100 × 5950
= 10 × 5950/100
= 59500/100 = $595
Thus, simple interest for 1 year = $595
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $595 × 9 = $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 6% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.
(2) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $8036 to clear the loan, then find the time period of the loan.
(3) How much loan did Daniel borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7625 to clear it?
(4) Find the amount to be paid if James borrowed a sum of $5000 at 8% simple interest for 8 years.
(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 4% simple interest for 7 years.
(6) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 3 years.
(8) If Joshua paid $5684 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 8 years.
(10) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6930 to clear the loan, then find the time period of the loan.