Question:
Find the amount to be paid if Thomas borrowed a sum of $5800 at 5% simple interest for 7 years.
Correct Answer
$7830
Solution And Explanation
Solution
Given,
Principal (P) = $5800
Rate of Simple Interest (SI) = 5%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 7
= $5800 ×5/100 × 7
= 5800 × 5 × 7/100
= 29000 × 7/100
= 203000/100
= $2030
Thus, Simple Interest = $2030
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 + $2030
= $7830
Thus, Amount to be paid = $7830 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) = 5%
And, Time (t) = 7 years
Thus, Amount (A)
= $5800 + ($5800 × 5% × 7)
= $5800 + ($5800 ×5/100 × 7)
= $5800 + (5800 × 5 × 7/100)
= $5800 + (29000 × 7/100)
= $5800 + (203000/100)
= $5800 + $2030 = $7830
Thus, Amount (A) to be paid = $7830 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5800, the simple interest in 1 year
= 5/100 × 5800
= 5 × 5800/100
= 29000/100 = $290
Thus, simple interest for 1 year = $290
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $290 × 7 = $2030
Thus, Simple Interest (SI) = $2030
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $2030
= $7830
Thus, Amount to be paid = $7830 Answer
Similar Questions
(1) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 3 years.
(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 4 years.
(3) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?
(4) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 8% simple interest?
(5) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 4% simple interest?
(6) If Joseph borrowed $3700 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 3 years.
(8) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 8 years.
(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 10% simple interest for 7 years.