Question:
Calculate the amount due if Robert borrowed a sum of $3100 at 8% simple interest for 3 years.
Correct Answer
$3844
Solution And Explanation
Solution
Given,
Principal (P) = $3100
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) = $3100 × 8% × 3
= $3100 ×8/100 × 3
= 3100 × 8 × 3/100
= 24800 × 3/100
= 74400/100
= $744
Thus, Simple Interest = $744
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 + $744
= $3844
Thus, Amount to be paid = $3844 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) = 3 years
Thus, Amount (A)
= $3100 + ($3100 × 8% × 3)
= $3100 + ($3100 ×8/100 × 3)
= $3100 + (3100 × 8 × 3/100)
= $3100 + (24800 × 3/100)
= $3100 + (74400/100)
= $3100 + $744 = $3844
Thus, Amount (A) to be paid = $3844 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 3 years
= Simple interest for 1 year × 3
= $248 × 3 = $744
Thus, Simple Interest (SI) = $744
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $744
= $3844
Thus, Amount to be paid = $3844 Answer
Similar Questions
(1) Margaret had to pay $4611 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(2) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 10% simple interest.
(3) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.
(4) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.
(5) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 5% simple interest?
(6) What amount will be due after 2 years if James borrowed a sum of $3000 at a 4% simple interest?
(7) Find the amount to be paid if John borrowed a sum of $5200 at 9% simple interest for 7 years.
(8) Mark had to pay $5060 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) If Sarah borrowed $3850 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.