Question:
Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 5% simple interest.
Correct Answer
$7650
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 5%
Time (t) = 10 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) = $5100 × 5% × 10
= $5100 ×5/100 × 10
= 5100 × 5 × 10/100
= 25500 × 10/100
= 255000/100
= $2550
Thus, Simple Interest = $2550
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 + $2550
= $7650
Thus, Amount to be paid = $7650 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) = 5%
And, Time (t) = 10 years
Thus, Amount (A)
= $5100 + ($5100 × 5% × 10)
= $5100 + ($5100 ×5/100 × 10)
= $5100 + (5100 × 5 × 10/100)
= $5100 + (25500 × 10/100)
= $5100 + (255000/100)
= $5100 + $2550 = $7650
Thus, Amount (A) to be paid = $7650 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 $5100, the simple interest in 1 year
= 5/100 × 5100
= 5 × 5100/100
= 25500/100 = $255
Thus, simple interest for 1 year = $255
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $255 × 10 = $2550
Thus, Simple Interest (SI) = $2550
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $2550
= $7650
Thus, Amount to be paid = $7650 Answer
Similar Questions
(1) Find the amount to be paid if Jessica borrowed a sum of $5750 at 10% simple interest for 7 years.
(2) In how much time a principal of $3100 will amount to $3348 at a simple interest of 4% per annum?
(3) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.
(4) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $11900 to clear the loan, then find the time period of the loan.
(5) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.
(6) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3150 will amount to $3654 at a simple interest of 4% per annum?
(8) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.
(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 8 years.
(10) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 3 years.