Question:
What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 8% simple interest?
Correct Answer
$4588
Solution And Explanation
Solution
Given,
Principal (P) = $3100
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) = $3100 × 8% × 6
= $3100 ×8/100 × 6
= 3100 × 8 × 6/100
= 24800 × 6/100
= 148800/100
= $1488
Thus, Simple Interest = $1488
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 = $3100 + $1488
= $4588
Thus, Amount to be paid = $4588 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 = $3100
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 6 years
Thus, Amount (A)
= $3100 + ($3100 × 8% × 6)
= $3100 + ($3100 ×8/100 × 6)
= $3100 + (3100 × 8 × 6/100)
= $3100 + (24800 × 6/100)
= $3100 + (148800/100)
= $3100 + $1488 = $4588
Thus, Amount (A) to be paid = $4588 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 $3100, the simple interest in 1 year
= 8/100 × 3100
= 8 × 3100/100
= 24800/100 = $248
Thus, simple interest for 1 year = $248
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $248 × 6 = $1488
Thus, Simple Interest (SI) = $1488
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $1488
= $4588
Thus, Amount to be paid = $4588 Answer
Similar Questions
(1) Calculate the amount due if Michael borrowed a sum of $3300 at 9% simple interest for 4 years.
(2) 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.
(3) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $10140 to clear the loan, then find the time period of the loan.
(4) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 3 years.
(6) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 6% simple interest.
(7) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 4 years.
(8) Michael had to pay $3696 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(9) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?
(10) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 4 years.