Question:
Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 7 years.
Correct Answer
$8424
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 8%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 7
= $5400 ×8/100 × 7
= 5400 × 8 × 7/100
= 43200 × 7/100
= 302400/100
= $3024
Thus, Simple Interest = $3024
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 + $3024
= $8424
Thus, Amount to be paid = $8424 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) = 8%
And, Time (t) = 7 years
Thus, Amount (A)
= $5400 + ($5400 × 8% × 7)
= $5400 + ($5400 ×8/100 × 7)
= $5400 + (5400 × 8 × 7/100)
= $5400 + (43200 × 7/100)
= $5400 + (302400/100)
= $5400 + $3024 = $8424
Thus, Amount (A) to be paid = $8424 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5400, the simple interest in 1 year
= 8/100 × 5400
= 8 × 5400/100
= 43200/100 = $432
Thus, simple interest for 1 year = $432
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $432 × 7 = $3024
Thus, Simple Interest (SI) = $3024
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $3024
= $8424
Thus, Amount to be paid = $8424 Answer
Similar Questions
(1) Calculate the amount due if Richard borrowed a sum of $3600 at 4% simple interest for 3 years.
(2) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 4 years.
(3) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 8 years.
(4) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 7 years.
(6) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.
(7) If James borrowed $3000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(8) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
(9) How much loan did Margaret borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6985 to clear it?
(10) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.