Question:
Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 7 years.
Correct Answer
$8642
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (SI) = 7%
Time (t) = 7 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% × 7
= $5800 ×7/100 × 7
= 5800 × 7 × 7/100
= 40600 × 7/100
= 284200/100
= $2842
Thus, Simple Interest = $2842
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 + $2842
= $8642
Thus, Amount to be paid = $8642 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) = 7 years
Thus, Amount (A)
= $5800 + ($5800 × 7% × 7)
= $5800 + ($5800 ×7/100 × 7)
= $5800 + (5800 × 7 × 7/100)
= $5800 + (40600 × 7/100)
= $5800 + (284200/100)
= $5800 + $2842 = $8642
Thus, Amount (A) to be paid = $8642 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 7 years
= Simple interest for 1 year × 7
= $406 × 7 = $2842
Thus, Simple Interest (SI) = $2842
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $2842
= $8642
Thus, Amount to be paid = $8642 Answer
Similar Questions
(1) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 4 years.
(3) If Michelle paid $5940 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(4) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6970 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 9% simple interest?
(6) Calculate the amount due if Linda borrowed a sum of $3350 at 9% simple interest for 3 years.
(7) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(8) 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.
(9) Find the amount to be paid if Sarah borrowed a sum of $5850 at 5% simple interest for 8 years.
(10) If Thomas paid $4560 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.