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) If Jessica paid $4500 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.
(4) If Susan paid $3942 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 3 years.
(6) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 6% simple interest?
(7) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
(8) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.
(10) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 2% simple interest.