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) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 6% simple interest?
(2) In how much time a principal of $3200 will amount to $3456 at a simple interest of 4% per annum?
(3) If Jennifer paid $3770 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $10080 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Jennifer borrowed a sum of $3250 at 5% simple interest for 4 years.
(6) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 9% simple interest.
(7) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(8) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6300 to clear it?
(9) Mary took a loan of $4100 at the rate of 8% simple interest per annum. If he paid an amount of $6068 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 7 years.