Question:
What amount does William have to pay after 6 years if he takes a loan of $3500 at 8% simple interest?
Correct Answer
$5180
Solution And Explanation
Solution
Given,
Principal (P) = $3500
Rate of Simple Interest (SI) = 8%
Time (t) = 6 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% × 6
= $3500 ×8/100 × 6
= 3500 × 8 × 6/100
= 28000 × 6/100
= 168000/100
= $1680
Thus, Simple Interest = $1680
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 + $1680
= $5180
Thus, Amount to be paid = $5180 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) = 6 years
Thus, Amount (A)
= $3500 + ($3500 × 8% × 6)
= $3500 + ($3500 ×8/100 × 6)
= $3500 + (3500 × 8 × 6/100)
= $3500 + (28000 × 6/100)
= $3500 + (168000/100)
= $3500 + $1680 = $5180
Thus, Amount (A) to be paid = $5180 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 6 years
= Simple interest for 1 year × 6
= $280 × 6 = $1680
Thus, Simple Interest (SI) = $1680
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3500 + $1680
= $5180
Thus, Amount to be paid = $5180 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
(2) Christopher had to pay $4360 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $9440 to clear the loan, then find the time period of the loan.
(4) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 7% simple interest?
(5) Calculate the amount due if Mary borrowed a sum of $3050 at 10% simple interest for 4 years.
(6) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $6846 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.
(8) Patricia had to pay $3622.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) In how much time a principal of $3150 will amount to $3465 at a simple interest of 5% per annum?
(10) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $7548 to clear the loan, then find the time period of the loan.