Question:
Calculate the amount due if Robert borrowed a sum of $3100 at 6% simple interest for 3 years.
Correct Answer
$3658
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 6%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 3
= $3100 ×6/100 × 3
= 3100 × 6 × 3/100
= 18600 × 3/100
= 55800/100
= $558
Thus, Simple Interest = $558
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 + $558
= $3658
Thus, Amount to be paid = $3658 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) = 6%
And, Time (t) = 3 years
Thus, Amount (A)
= $3100 + ($3100 × 6% × 3)
= $3100 + ($3100 ×6/100 × 3)
= $3100 + (3100 × 6 × 3/100)
= $3100 + (18600 × 3/100)
= $3100 + (55800/100)
= $3100 + $558 = $3658
Thus, Amount (A) to be paid = $3658 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $3100, the simple interest in 1 year
= 6/100 × 3100
= 6 × 3100/100
= 18600/100 = $186
Thus, simple interest for 1 year = $186
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $186 × 3 = $558
Thus, Simple Interest (SI) = $558
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $558
= $3658
Thus, Amount to be paid = $3658 Answer
Similar Questions
(1) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $12200 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 10% simple interest.
(3) How much loan did Timothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8510 to clear it?
(4) Jessica had to pay $4200 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 4 years.
(7) What amount does Robert have to pay after 6 years if he takes a loan of $3100 at 7% simple interest?
(8) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 3% simple interest.
(9) How much loan did William borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6050 to clear it?
(10) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.