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) Calculate the amount due if John borrowed a sum of $3200 at 9% simple interest for 4 years.
(2) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 7% simple interest?
(3) If Thomas borrowed $3800 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(4) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 5% simple interest?
(6) Sarah took a loan of $5700 at the rate of 9% simple interest per annum. If he paid an amount of $10830 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 7% simple interest?
(8) Linda took a loan of $4700 at the rate of 8% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 9% simple interest for 8 years.
(10) If Jennifer borrowed $3250 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.