Question:
Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 4% simple interest.
Correct Answer
$7140
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 4%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 10
= $5100 ×4/100 × 10
= 5100 × 4 × 10/100
= 20400 × 10/100
= 204000/100
= $2040
Thus, Simple Interest = $2040
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 + $2040
= $7140
Thus, Amount to be paid = $7140 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) = 4%
And, Time (t) = 10 years
Thus, Amount (A)
= $5100 + ($5100 × 4% × 10)
= $5100 + ($5100 ×4/100 × 10)
= $5100 + (5100 × 4 × 10/100)
= $5100 + (20400 × 10/100)
= $5100 + (204000/100)
= $5100 + $2040 = $7140
Thus, Amount (A) to be paid = $7140 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5100, the simple interest in 1 year
= 4/100 × 5100
= 4 × 5100/100
= 20400/100 = $204
Thus, simple interest for 1 year = $204
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $204 × 10 = $2040
Thus, Simple Interest (SI) = $2040
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $2040
= $7140
Thus, Amount to be paid = $7140 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $10332 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 7 years.
(3) How much loan did Linda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6152.5 to clear it?
(4) Calculate the amount due if Richard borrowed a sum of $3600 at 7% simple interest for 4 years.
(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 7 years.
(6) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.
(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 9% simple interest for 7 years.
(8) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 5% simple interest.
(9) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7421 to clear the loan, then find the time period of the loan.
(10) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.