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) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 7 years.
(2) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $8772 to clear the loan, then find the time period of the loan.
(3) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.
(5) 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.
(6) Mark had to pay $4928 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) In how much time a principal of $3050 will amount to $3416 at a simple interest of 3% per annum?
(8) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 8 years.
(9) What amount does John have to pay after 6 years if he takes a loan of $3200 at 3% simple interest?
(10) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.