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) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.
(2) Elizabeth took a loan of $4900 at the rate of 10% simple interest per annum. If he paid an amount of $9800 to clear the loan, then find the time period of the loan.
(3) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 10% simple interest?
(4) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 7% simple interest.
(5) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 8% simple interest.
(6) Calculate the amount due if Barbara borrowed a sum of $3550 at 9% simple interest for 4 years.
(7) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10132 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Joseph borrowed a sum of $3700 at 7% simple interest for 4 years.
(9) Matthew had to pay $4578 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.