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) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.
(2) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $5712 to clear the loan, then find the time period of the loan.
(3) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7544 to clear the loan, then find the time period of the loan.
(4) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6248 to clear the loan, then find the time period of the loan.
(5) How much loan did Melissa borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9187.5 to clear it?
(6) How much loan did Jacob borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9200 to clear it?
(7) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.
(8) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $8330 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.
(10) Find the amount to be paid if Sarah borrowed a sum of $5850 at 9% simple interest for 8 years.