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) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 7% simple interest.
(2) Robert took a loan of $4200 at the rate of 8% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.
(3) 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.
(4) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $8313 to clear the loan, then find the time period of the loan.
(5) How much loan did Thomas borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7250 to clear it?
(6) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 5% simple interest?
(7) If Andrew paid $5568 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(8) John had to pay $3680 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 6% simple interest.
(10) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $10472 to clear the loan, then find the time period of the loan.