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) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $8520 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 10% simple interest.
(3) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.
(4) Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 3 years.
(5) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.
(6) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.
(7) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.
(8) If Jennifer paid $3510 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 does Michael have to pay after 6 years if he takes a loan of $3300 at 7% simple interest?
(10) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 8% simple interest?