Question:
Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 7 years.
Correct Answer
$9860
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (SI) = 10%
Time (t) = 7 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% × 7
= $5800 ×10/100 × 7
= 5800 × 10 × 7/100
= 58000 × 7/100
= 406000/100
= $4060
Thus, Simple Interest = $4060
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 + $4060
= $9860
Thus, Amount to be paid = $9860 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) = 7 years
Thus, Amount (A)
= $5800 + ($5800 × 10% × 7)
= $5800 + ($5800 ×10/100 × 7)
= $5800 + (5800 × 10 × 7/100)
= $5800 + (58000 × 7/100)
= $5800 + (406000/100)
= $5800 + $4060 = $9860
Thus, Amount (A) to be paid = $9860 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 7 years
= Simple interest for 1 year × 7
= $580 × 7 = $4060
Thus, Simple Interest (SI) = $4060
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $4060
= $9860
Thus, Amount to be paid = $9860 Answer
Similar Questions
(1) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7872 to clear the loan, then find the time period of the loan.
(2) Donald took a loan of $7000 at the rate of 6% simple interest per annum. If he paid an amount of $11200 to clear the loan, then find the time period of the loan.
(3) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $8150 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 8 years.
(5) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 8% simple interest for 7 years.
(6) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.
(7) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 4% simple interest?
(8) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 7% simple interest?
(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 7 years.