Question:
Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.
Correct Answer
$6018
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 2%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 9
= $5100 ×2/100 × 9
= 5100 × 2 × 9/100
= 10200 × 9/100
= 91800/100
= $918
Thus, Simple Interest = $918
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 + $918
= $6018
Thus, Amount to be paid = $6018 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) = 2%
And, Time (t) = 9 years
Thus, Amount (A)
= $5100 + ($5100 × 2% × 9)
= $5100 + ($5100 ×2/100 × 9)
= $5100 + (5100 × 2 × 9/100)
= $5100 + (10200 × 9/100)
= $5100 + (91800/100)
= $5100 + $918 = $6018
Thus, Amount (A) to be paid = $6018 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5100, the simple interest in 1 year
= 2/100 × 5100
= 2 × 5100/100
= 10200/100 = $102
Thus, simple interest for 1 year = $102
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $102 × 9 = $918
Thus, Simple Interest (SI) = $918
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $918
= $6018
Thus, Amount to be paid = $6018 Answer
Similar Questions
(1) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $8778 to clear the loan, then find the time period of the loan.
(2) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 4 years.
(4) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 8 years.
(5) Ashley had to pay $4959.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(6) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $8200 to clear the loan, then find the time period of the loan.
(7) Sarah had to pay $4196.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(8) Karen had to pay $4542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Find the amount to be paid if Susan borrowed a sum of $5650 at 9% simple interest for 7 years.
(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 7 years.