Question:
Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 7 years.
Correct Answer
$5814
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 2%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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) = $5100 × 2% × 7
= $5100 ×2/100 × 7
= 5100 × 2 × 7/100
= 10200 × 7/100
= 71400/100
= $714
Thus, Simple Interest = $714
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 = $5100 + $714
= $5814
Thus, Amount to be paid = $5814 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 = $5100
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 7 years
Thus, Amount (A)
= $5100 + ($5100 × 2% × 7)
= $5100 + ($5100 ×2/100 × 7)
= $5100 + (5100 × 2 × 7/100)
= $5100 + (10200 × 7/100)
= $5100 + (71400/100)
= $5100 + $714 = $5814
Thus, Amount (A) to be paid = $5814 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5100, the simple interest in 1 year
= 2/100 × 5100
= 2 × 5100/100
= 10200/100 = $102
Thus, simple interest for 1 year = $102
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $102 × 7 = $714
Thus, Simple Interest (SI) = $714
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $714
= $5814
Thus, Amount to be paid = $5814 Answer
Similar Questions
(1) Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 7 years.
(2) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 4% simple interest.
(4) In how much time a principal of $3000 will amount to $3750 at a simple interest of 5% per annum?
(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 4% simple interest for 4 years.
(6) Michael had to pay $3498 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(7) How much loan did Ronald borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8250 to clear it?
(8) Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 3 years.
(9) What amount does William have to pay after 6 years if he takes a loan of $3500 at 10% simple interest?
(10) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.