Question:
Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.
Correct Answer
$8627.5
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 5%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 9
= $5950 ×5/100 × 9
= 5950 × 5 × 9/100
= 29750 × 9/100
= 267750/100
= $2677.5
Thus, Simple Interest = $2677.5
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 + $2677.5
= $8627.5
Thus, Amount to be paid = $8627.5 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) = 5%
And, Time (t) = 9 years
Thus, Amount (A)
= $5950 + ($5950 × 5% × 9)
= $5950 + ($5950 ×5/100 × 9)
= $5950 + (5950 × 5 × 9/100)
= $5950 + (29750 × 9/100)
= $5950 + (267750/100)
= $5950 + $2677.5 = $8627.5
Thus, Amount (A) to be paid = $8627.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5950, the simple interest in 1 year
= 5/100 × 5950
= 5 × 5950/100
= 29750/100 = $297.5
Thus, simple interest for 1 year = $297.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $297.5 × 9 = $2677.5
Thus, Simple Interest (SI) = $2677.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $2677.5
= $8627.5
Thus, Amount to be paid = $8627.5 Answer
Similar Questions
(1) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
(2) How much loan did George borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9125 to clear it?
(3) Susan took a loan of $5300 at the rate of 8% simple interest per annum. If he paid an amount of $8268 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if Richard borrowed a sum of $3600 at 8% simple interest for 3 years.
(5) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.
(6) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 4% simple interest?
(8) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 4% simple interest?
(9) Charles took a loan of $5800 at the rate of 9% simple interest per annum. If he paid an amount of $9454 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 3% simple interest.