Question:
Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.
Correct Answer
$11020
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (SI) = 10%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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) = $5800 × 10% × 9
= $5800 ×10/100 × 9
= 5800 × 10 × 9/100
= 58000 × 9/100
= 522000/100
= $5220
Thus, Simple Interest = $5220
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 = $5800 + $5220
= $11020
Thus, Amount to be paid = $11020 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 = $5800
Rate of Simple Interest (SI) or (R) = 10%
And, Time (t) = 9 years
Thus, Amount (A)
= $5800 + ($5800 × 10% × 9)
= $5800 + ($5800 ×10/100 × 9)
= $5800 + (5800 × 10 × 9/100)
= $5800 + (58000 × 9/100)
= $5800 + (522000/100)
= $5800 + $5220 = $11020
Thus, Amount (A) to be paid = $11020 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5800, the simple interest in 1 year
= 10/100 × 5800
= 10 × 5800/100
= 58000/100 = $580
Thus, simple interest for 1 year = $580
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $580 × 9 = $5220
Thus, Simple Interest (SI) = $5220
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $5220
= $11020
Thus, Amount to be paid = $11020 Answer
Similar Questions
(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 8 years.
(2) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 3 years.
(3) What amount will be due after 2 years if Joshua borrowed a sum of $3950 at a 5% simple interest?
(4) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 3% simple interest.
(5) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.
(6) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $11480 to clear the loan, then find the time period of the loan.
(7) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 7% simple interest?
(9) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.
(10) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 9% simple interest?