Question:
Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 8% simple interest.
Correct Answer
$9720
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 8%
Time (t) = 10 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% × 10
= $5400 ×8/100 × 10
= 5400 × 8 × 10/100
= 43200 × 10/100
= 432000/100
= $4320
Thus, Simple Interest = $4320
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 + $4320
= $9720
Thus, Amount to be paid = $9720 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) = 10 years
Thus, Amount (A)
= $5400 + ($5400 × 8% × 10)
= $5400 + ($5400 ×8/100 × 10)
= $5400 + (5400 × 8 × 10/100)
= $5400 + (43200 × 10/100)
= $5400 + (432000/100)
= $5400 + $4320 = $9720
Thus, Amount (A) to be paid = $9720 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 10 years
= Simple interest for 1 year × 10
= $432 × 10 = $4320
Thus, Simple Interest (SI) = $4320
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $4320
= $9720
Thus, Amount to be paid = $9720 Answer
Similar Questions
(1) Calculate the amount due if Mary borrowed a sum of $3050 at 9% simple interest for 4 years.
(2) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 5% simple interest?
(4) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5964 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 10% simple interest?
(6) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 8% simple interest?
(7) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 4 years.
(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 4 years.
(9) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 10% simple interest?
(10) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7602 to clear the loan, then find the time period of the loan.