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 Charles borrowed a sum of $5900 at 3% simple interest for 8 years.
(2) How much loan did Michael borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6625 to clear it?
(3) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9834 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 8 years.
(5) 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.
(6) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.
(7) Karen took a loan of $5900 at the rate of 7% simple interest per annum. If he paid an amount of $8378 to clear the loan, then find the time period of the loan.
(8) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7661 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 7 years.
(10) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.