Question:
Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 9% simple interest.
Correct Answer
$10260
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 9%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 10
= $5400 ×9/100 × 10
= 5400 × 9 × 10/100
= 48600 × 10/100
= 486000/100
= $4860
Thus, Simple Interest = $4860
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 + $4860
= $10260
Thus, Amount to be paid = $10260 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) = 9%
And, Time (t) = 10 years
Thus, Amount (A)
= $5400 + ($5400 × 9% × 10)
= $5400 + ($5400 ×9/100 × 10)
= $5400 + (5400 × 9 × 10/100)
= $5400 + (48600 × 10/100)
= $5400 + (486000/100)
= $5400 + $4860 = $10260
Thus, Amount (A) to be paid = $10260 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5400, the simple interest in 1 year
= 9/100 × 5400
= 9 × 5400/100
= 48600/100 = $486
Thus, simple interest for 1 year = $486
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $486 × 10 = $4860
Thus, Simple Interest (SI) = $4860
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $4860
= $10260
Thus, Amount to be paid = $10260 Answer
Similar Questions
(1) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 10% simple interest?
(2) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 9% simple interest?
(3) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $8236 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 3% simple interest.
(5) 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.
(6) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7176 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 6% simple interest?
(8) If Michael borrowed $3300 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(9) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 4 years.
(10) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.