Question:
Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 8 years.
Correct Answer
$6696
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 3%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 8
= $5400 ×3/100 × 8
= 5400 × 3 × 8/100
= 16200 × 8/100
= 129600/100
= $1296
Thus, Simple Interest = $1296
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 + $1296
= $6696
Thus, Amount to be paid = $6696 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) = 3%
And, Time (t) = 8 years
Thus, Amount (A)
= $5400 + ($5400 × 3% × 8)
= $5400 + ($5400 ×3/100 × 8)
= $5400 + (5400 × 3 × 8/100)
= $5400 + (16200 × 8/100)
= $5400 + (129600/100)
= $5400 + $1296 = $6696
Thus, Amount (A) to be paid = $6696 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5400, the simple interest in 1 year
= 3/100 × 5400
= 3 × 5400/100
= 16200/100 = $162
Thus, simple interest for 1 year = $162
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $162 × 8 = $1296
Thus, Simple Interest (SI) = $1296
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $1296
= $6696
Thus, Amount to be paid = $6696 Answer
Similar Questions
(1) Calculate the amount due if Thomas borrowed a sum of $3800 at 5% simple interest for 4 years.
(2) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 5% per annum?
(3) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 3 years.
(4) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.
(5) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9880 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 7% simple interest.
(7) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 5% simple interest.
(8) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $10921 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if James borrowed a sum of $5000 at 9% simple interest for 7 years.
(10) Robert took a loan of $4200 at the rate of 10% simple interest per annum. If he paid an amount of $6720 to clear the loan, then find the time period of the loan.