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) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.
(2) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 5% simple interest?
(3) What amount does David have to pay after 5 years if he takes a loan of $3400 at 10% simple interest?
(4) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 7% simple interest?
(5) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.
(6) Calculate the amount due if Susan borrowed a sum of $3650 at 4% simple interest for 4 years.
(7) In how much time a principal of $3000 will amount to $3270 at a simple interest of 3% per annum?
(8) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 9% simple interest?
(9) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 8 years.
(10) Calculate the amount due if Linda borrowed a sum of $3350 at 2% simple interest for 4 years.