Question:
Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 8% simple interest.
Correct Answer
$8600
Solution And Explanation
Solution
Given,
Principal (P) = $5000
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) = $5000 × 8% × 9
= $5000 ×8/100 × 9
= 5000 × 8 × 9/100
= 40000 × 9/100
= 360000/100
= $3600
Thus, Simple Interest = $3600
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 = $5000 + $3600
= $8600
Thus, Amount to be paid = $8600 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 = $5000
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 9 years
Thus, Amount (A)
= $5000 + ($5000 × 8% × 9)
= $5000 + ($5000 ×8/100 × 9)
= $5000 + (5000 × 8 × 9/100)
= $5000 + (40000 × 9/100)
= $5000 + (360000/100)
= $5000 + $3600 = $8600
Thus, Amount (A) to be paid = $8600 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 $5000, the simple interest in 1 year
= 8/100 × 5000
= 8 × 5000/100
= 40000/100 = $400
Thus, simple interest for 1 year = $400
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $400 × 9 = $3600
Thus, Simple Interest (SI) = $3600
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5000 + $3600
= $8600
Thus, Amount to be paid = $8600 Answer
Similar Questions
(1) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(2) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $7544 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 9% simple interest?
(4) What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 7% simple interest?
(5) 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.
(6) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 4% simple interest for 7 years.
(7) Richard had to pay $4032 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 4 years.
(9) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 6% simple interest.
(10) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $6956 to clear the loan, then find the time period of the loan.