Question:
Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 6% simple interest.
Correct Answer
$8316
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 6%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 9
= $5400 ×6/100 × 9
= 5400 × 6 × 9/100
= 32400 × 9/100
= 291600/100
= $2916
Thus, Simple Interest = $2916
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 + $2916
= $8316
Thus, Amount to be paid = $8316 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) = 6%
And, Time (t) = 9 years
Thus, Amount (A)
= $5400 + ($5400 × 6% × 9)
= $5400 + ($5400 ×6/100 × 9)
= $5400 + (5400 × 6 × 9/100)
= $5400 + (32400 × 9/100)
= $5400 + (291600/100)
= $5400 + $2916 = $8316
Thus, Amount (A) to be paid = $8316 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5400, the simple interest in 1 year
= 6/100 × 5400
= 6 × 5400/100
= 32400/100 = $324
Thus, simple interest for 1 year = $324
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $324 × 9 = $2916
Thus, Simple Interest (SI) = $2916
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $2916
= $8316
Thus, Amount to be paid = $8316 Answer
Similar Questions
(1) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 4% simple interest.
(2) Sandra had to pay $4717 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) Charles had to pay $4485 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 7 years.
(5) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 8% simple interest?
(6) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 4 years.
(7) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 4% simple interest?
(8) If Mary paid $3294 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 7% simple interest?
(10) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 9% simple interest.