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) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 8% simple interest?
(2) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(3) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $8732 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 5% simple interest.
(5) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 6% simple interest?
(6) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.
(7) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 7 years.
(8) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $8869 to clear the loan, then find the time period of the loan.
(9) Donald took a loan of $7000 at the rate of 10% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 7% simple interest?