Question:
Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 7% simple interest.
Correct Answer
$9860
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (SI) = 7%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 10
= $5800 ×7/100 × 10
= 5800 × 7 × 10/100
= 40600 × 10/100
= 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) = 7%
And, Time (t) = 10 years
Thus, Amount (A)
= $5800 + ($5800 × 7% × 10)
= $5800 + ($5800 ×7/100 × 10)
= $5800 + (5800 × 7 × 10/100)
= $5800 + (40600 × 10/100)
= $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 = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5800, the simple interest in 1 year
= 7/100 × 5800
= 7 × 5800/100
= 40600/100 = $406
Thus, simple interest for 1 year = $406
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $406 × 10 = $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) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.
(2) Calculate the amount due if Jennifer borrowed a sum of $3250 at 2% simple interest for 3 years.
(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 7 years.
(4) Find the amount to be paid if James borrowed a sum of $5000 at 5% simple interest for 7 years.
(5) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $9600 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 4 years.
(7) If Daniel paid $4756 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 7% simple interest.
(9) Nancy took a loan of $6300 at the rate of 10% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.
(10) How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?