Question:
Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 3 years.
Correct Answer
$3751
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 7%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 3
= $3100 ×7/100 × 3
= 3100 × 7 × 3/100
= 21700 × 3/100
= 65100/100
= $651
Thus, Simple Interest = $651
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 + $651
= $3751
Thus, Amount to be paid = $3751 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) = 7%
And, Time (t) = 3 years
Thus, Amount (A)
= $3100 + ($3100 × 7% × 3)
= $3100 + ($3100 ×7/100 × 3)
= $3100 + (3100 × 7 × 3/100)
= $3100 + (21700 × 3/100)
= $3100 + (65100/100)
= $3100 + $651 = $3751
Thus, Amount (A) to be paid = $3751 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3100, the simple interest in 1 year
= 7/100 × 3100
= 7 × 3100/100
= 21700/100 = $217
Thus, simple interest for 1 year = $217
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $217 × 3 = $651
Thus, Simple Interest (SI) = $651
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $651
= $3751
Thus, Amount to be paid = $3751 Answer
Similar Questions
(1) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3200 will amount to $3712 at a simple interest of 4% per annum?
(3) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6400 to clear the loan, then find the time period of the loan.
(4) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9656 to clear the loan, then find the time period of the loan.
(5) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?
(6) Calculate the amount due if Jessica borrowed a sum of $3750 at 4% simple interest for 3 years.
(7) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.
(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 2% simple interest for 8 years.
(9) If Patricia borrowed $3150 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) Margaret took a loan of $6700 at the rate of 7% simple interest per annum. If he paid an amount of $11390 to clear the loan, then find the time period of the loan.