Question:
Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.
Correct Answer
$8772
Solution And Explanation
Solution
Given,
Principal (P) = $5100
Rate of Simple Interest (SI) = 8%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 9
= $5100 ×8/100 × 9
= 5100 × 8 × 9/100
= 40800 × 9/100
= 367200/100
= $3672
Thus, Simple Interest = $3672
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 + $3672
= $8772
Thus, Amount to be paid = $8772 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) = 8%
And, Time (t) = 9 years
Thus, Amount (A)
= $5100 + ($5100 × 8% × 9)
= $5100 + ($5100 ×8/100 × 9)
= $5100 + (5100 × 8 × 9/100)
= $5100 + (40800 × 9/100)
= $5100 + (367200/100)
= $5100 + $3672 = $8772
Thus, Amount (A) to be paid = $8772 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5100, the simple interest in 1 year
= 8/100 × 5100
= 8 × 5100/100
= 40800/100 = $408
Thus, simple interest for 1 year = $408
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $408 × 9 = $3672
Thus, Simple Interest (SI) = $3672
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5100 + $3672
= $8772
Thus, Amount to be paid = $8772 Answer
Similar Questions
(1) What amount does David have to pay after 6 years if he takes a loan of $3400 at 9% simple interest?
(2) If James paid $3480 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(3) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.
(4) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.
(5) James took a loan of $4000 at the rate of 10% simple interest per annum. If he paid an amount of $7600 to clear the loan, then find the time period of the loan.
(6) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(7) How much loan did David borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6750 to clear it?
(8) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 8 years.
(9) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.
(10) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8944 to clear the loan, then find the time period of the loan.