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 John borrowed a sum of $5200 at 10% simple interest for 7 years.
(2) In how much time a principal of $3000 will amount to $3180 at a simple interest of 3% per annum?
(3) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7987 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 7 years.
(5) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.
(6) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 7% simple interest?
(7) What amount does William have to pay after 6 years if he takes a loan of $3500 at 3% simple interest?
(8) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12308 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 9% simple interest for 3 years.
(10) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 3% simple interest.