Question:
Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.
Correct Answer
$7854
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 6%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 9
= $5100 ×6/100 × 9
= 5100 × 6 × 9/100
= 30600 × 9/100
= 275400/100
= $2754
Thus, Simple Interest = $2754
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 + $2754
= $7854
Thus, Amount to be paid = $7854 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) = 6%
And, Time (t) = 9 years
Thus, Amount (A)
= $5100 + ($5100 × 6% × 9)
= $5100 + ($5100 ×6/100 × 9)
= $5100 + (5100 × 6 × 9/100)
= $5100 + (30600 × 9/100)
= $5100 + (275400/100)
= $5100 + $2754 = $7854
Thus, Amount (A) to be paid = $7854 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5100, the simple interest in 1 year
= 6/100 × 5100
= 6 × 5100/100
= 30600/100 = $306
Thus, simple interest for 1 year = $306
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $306 × 9 = $2754
Thus, Simple Interest (SI) = $2754
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $2754
= $7854
Thus, Amount to be paid = $7854 Answer
Similar Questions
(1) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 8 years.
(2) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10836 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.
(4) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8965 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
(6) What amount does James have to pay after 6 years if he takes a loan of $3000 at 9% simple interest?
(7) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.
(8) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 4 years.
(9) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 4% simple interest?
(10) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 4 years.