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) Calculate the amount due if Charles borrowed a sum of $3900 at 5% simple interest for 3 years.
(2) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 8 years.
(3) In how much time a principal of $3050 will amount to $3355 at a simple interest of 2% per annum?
(4) Calculate the amount due if Patricia borrowed a sum of $3150 at 8% simple interest for 4 years.
(5) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 4 years.
(6) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $6512 to clear the loan, then find the time period of the loan.
(7) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.
(9) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 4 years.
(10) What amount does David have to pay after 5 years if he takes a loan of $3400 at 9% simple interest?