Question:
Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 7% simple interest.
Correct Answer
$8802
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 7%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 9
= $5400 ×7/100 × 9
= 5400 × 7 × 9/100
= 37800 × 9/100
= 340200/100
= $3402
Thus, Simple Interest = $3402
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 + $3402
= $8802
Thus, Amount to be paid = $8802 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) = 7%
And, Time (t) = 9 years
Thus, Amount (A)
= $5400 + ($5400 × 7% × 9)
= $5400 + ($5400 ×7/100 × 9)
= $5400 + (5400 × 7 × 9/100)
= $5400 + (37800 × 9/100)
= $5400 + (340200/100)
= $5400 + $3402 = $8802
Thus, Amount (A) to be paid = $8802 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5400, the simple interest in 1 year
= 7/100 × 5400
= 7 × 5400/100
= 37800/100 = $378
Thus, simple interest for 1 year = $378
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $378 × 9 = $3402
Thus, Simple Interest (SI) = $3402
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $3402
= $8802
Thus, Amount to be paid = $8802 Answer
Similar Questions
(1) If William paid $4060 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(2) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 6% simple interest?
(3) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10860 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 8 years.
(5) What amount does William have to pay after 6 years if he takes a loan of $3500 at 7% simple interest?
(6) Find the amount to be paid if Karen borrowed a sum of $5950 at 7% simple interest for 7 years.
(7) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 8 years.
(8) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.
(9) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 8 years.
(10) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $11152 to clear the loan, then find the time period of the loan.