Question:
Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 3 years.
Correct Answer
$4340
Solution And Explanation
Solution
Given,
Principal (P) = $3500
Rate of Simple Interest (SI) = 8%
Time (t) = 3 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) = $3500 × 8% × 3
= $3500 ×8/100 × 3
= 3500 × 8 × 3/100
= 28000 × 3/100
= 84000/100
= $840
Thus, Simple Interest = $840
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 = $3500 + $840
= $4340
Thus, Amount to be paid = $4340 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 = $3500
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 3 years
Thus, Amount (A)
= $3500 + ($3500 × 8% × 3)
= $3500 + ($3500 ×8/100 × 3)
= $3500 + (3500 × 8 × 3/100)
= $3500 + (28000 × 3/100)
= $3500 + (84000/100)
= $3500 + $840 = $4340
Thus, Amount (A) to be paid = $4340 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 $3500, the simple interest in 1 year
= 8/100 × 3500
= 8 × 3500/100
= 28000/100 = $280
Thus, simple interest for 1 year = $280
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $280 × 3 = $840
Thus, Simple Interest (SI) = $840
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3500 + $840
= $4340
Thus, Amount to be paid = $4340 Answer
Similar Questions
(1) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $6256 to clear the loan, then find the time period of the loan.
(2) Paul had to pay $4982 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(3) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $6880 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 4 years.
(5) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 10% simple interest?
(6) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7450 to clear the loan, then find the time period of the loan.
(7) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $7238 to clear the loan, then find the time period of the loan.
(8) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $7700 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if Paul borrowed a sum of $3850 at a 10% simple interest?
(10) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 8 years.