Question:
Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 5% simple interest.
Correct Answer
$7830
Solution And Explanation
Solution
Given,
Principal (P) = $5400
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) = $5400 × 5% × 9
= $5400 ×5/100 × 9
= 5400 × 5 × 9/100
= 27000 × 9/100
= 243000/100
= $2430
Thus, Simple Interest = $2430
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 = $5400 + $2430
= $7830
Thus, Amount to be paid = $7830 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 = $5400
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 9 years
Thus, Amount (A)
= $5400 + ($5400 × 5% × 9)
= $5400 + ($5400 ×5/100 × 9)
= $5400 + (5400 × 5 × 9/100)
= $5400 + (27000 × 9/100)
= $5400 + (243000/100)
= $5400 + $2430 = $7830
Thus, Amount (A) to be paid = $7830 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 $5400, the simple interest in 1 year
= 5/100 × 5400
= 5 × 5400/100
= 27000/100 = $270
Thus, simple interest for 1 year = $270
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $270 × 9 = $2430
Thus, Simple Interest (SI) = $2430
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $2430
= $7830
Thus, Amount to be paid = $7830 Answer
Similar Questions
(1) Susan took a loan of $5300 at the rate of 7% simple interest per annum. If he paid an amount of $7526 to clear the loan, then find the time period of the loan.
(2) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 6% simple interest?
(3) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 7% simple interest.
(4) Susan took a loan of $5300 at the rate of 9% simple interest per annum. If he paid an amount of $8639 to clear the loan, then find the time period of the loan.
(5) Linda had to pay $3752 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 3% simple interest?
(7) Joseph took a loan of $5400 at the rate of 7% simple interest per annum. If he paid an amount of $8802 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 4 years.
(9) Joseph had to pay $3922 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) What amount does David have to pay after 6 years if he takes a loan of $3400 at 5% simple interest?