Question:
Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 6% simple interest.
Correct Answer
$8640
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 6%
Time (t) = 10 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% × 10
= $5400 ×6/100 × 10
= 5400 × 6 × 10/100
= 32400 × 10/100
= 324000/100
= $3240
Thus, Simple Interest = $3240
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 + $3240
= $8640
Thus, Amount to be paid = $8640 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) = 10 years
Thus, Amount (A)
= $5400 + ($5400 × 6% × 10)
= $5400 + ($5400 ×6/100 × 10)
= $5400 + (5400 × 6 × 10/100)
= $5400 + (32400 × 10/100)
= $5400 + (324000/100)
= $5400 + $3240 = $8640
Thus, Amount (A) to be paid = $8640 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 10 years
= Simple interest for 1 year × 10
= $324 × 10 = $3240
Thus, Simple Interest (SI) = $3240
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $3240
= $8640
Thus, Amount to be paid = $8640 Answer
Similar Questions
(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 5% simple interest for 3 years.
(2) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.
(3) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 4% simple interest?
(4) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $8480 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 8 years.
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 3% simple interest for 7 years.
(8) Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 4 years.
(9) If Sarah paid $4312 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(10) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 10% simple interest?