Question:
Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 7 years.
Correct Answer
$7290
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 5%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 7
= $5400 ×5/100 × 7
= 5400 × 5 × 7/100
= 27000 × 7/100
= 189000/100
= $1890
Thus, Simple Interest = $1890
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 + $1890
= $7290
Thus, Amount to be paid = $7290 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) = 5%
And, Time (t) = 7 years
Thus, Amount (A)
= $5400 + ($5400 × 5% × 7)
= $5400 + ($5400 ×5/100 × 7)
= $5400 + (5400 × 5 × 7/100)
= $5400 + (27000 × 7/100)
= $5400 + (189000/100)
= $5400 + $1890 = $7290
Thus, Amount (A) to be paid = $7290 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5400, the simple interest in 1 year
= 5/100 × 5400
= 5 × 5400/100
= 27000/100 = $270
Thus, simple interest for 1 year = $270
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $270 × 7 = $1890
Thus, Simple Interest (SI) = $1890
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $1890
= $7290
Thus, Amount to be paid = $7290 Answer
Similar Questions
(1) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 7 years.
(2) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
(3) Find the amount to be paid if William borrowed a sum of $5500 at 3% simple interest for 7 years.
(4) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 8% simple interest.
(5) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $11210 to clear the loan, then find the time period of the loan.
(6) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7100 to clear the loan, then find the time period of the loan.
(7) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $12600 to clear the loan, then find the time period of the loan.
(8) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 4% simple interest?
(9) Calculate the amount due if Patricia borrowed a sum of $3150 at 2% simple interest for 4 years.
(10) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 3 years.