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) What amount does James have to pay after 6 years if he takes a loan of $3000 at 10% simple interest?
(2) Calculate the amount due if Charles borrowed a sum of $3900 at 7% simple interest for 4 years.
(3) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $6390 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 2% simple interest for 8 years.
(5) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 9% simple interest?
(6) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 5% simple interest?
(7) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.
(8) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 4% simple interest.
(9) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 3 years.
(10) In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?