Question:
Find the amount to be paid if Robert borrowed a sum of $5100 at 5% simple interest for 7 years.
Correct Answer
$6885
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 5%
Time (t) = 7 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% × 7
= $5100 ×5/100 × 7
= 5100 × 5 × 7/100
= 25500 × 7/100
= 178500/100
= $1785
Thus, Simple Interest = $1785
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 + $1785
= $6885
Thus, Amount to be paid = $6885 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) = 7 years
Thus, Amount (A)
= $5100 + ($5100 × 5% × 7)
= $5100 + ($5100 ×5/100 × 7)
= $5100 + (5100 × 5 × 7/100)
= $5100 + (25500 × 7/100)
= $5100 + (178500/100)
= $5100 + $1785 = $6885
Thus, Amount (A) to be paid = $6885 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 7 years
= Simple interest for 1 year × 7
= $255 × 7 = $1785
Thus, Simple Interest (SI) = $1785
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $1785
= $6885
Thus, Amount to be paid = $6885 Answer
Similar Questions
(1) Jennifer had to pay $3445 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 3 years.
(4) Calculate the amount due if Robert borrowed a sum of $3100 at 9% simple interest for 4 years.
(5) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10148 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Joseph borrowed a sum of $3700 at 6% simple interest for 4 years.
(7) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.
(8) Calculate the amount due if John borrowed a sum of $3200 at 10% simple interest for 4 years.
(9) William took a loan of $5000 at the rate of 6% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(10) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.