Question:
Calculate the amount due if Robert borrowed a sum of $3100 at 2% simple interest for 3 years.
Correct Answer
$3286
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 2%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 3
= $3100 ×2/100 × 3
= 3100 × 2 × 3/100
= 6200 × 3/100
= 18600/100
= $186
Thus, Simple Interest = $186
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 + $186
= $3286
Thus, Amount to be paid = $3286 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) = 2%
And, Time (t) = 3 years
Thus, Amount (A)
= $3100 + ($3100 × 2% × 3)
= $3100 + ($3100 ×2/100 × 3)
= $3100 + (3100 × 2 × 3/100)
= $3100 + (6200 × 3/100)
= $3100 + (18600/100)
= $3100 + $186 = $3286
Thus, Amount (A) to be paid = $3286 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $3100, the simple interest in 1 year
= 2/100 × 3100
= 2 × 3100/100
= 6200/100 = $62
Thus, simple interest for 1 year = $62
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $62 × 3 = $186
Thus, Simple Interest (SI) = $186
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $186
= $3286
Thus, Amount to be paid = $3286 Answer
Similar Questions
(1) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9142.5 to clear it?
(2) If Barbara borrowed $3550 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(3) If Christopher paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 10% simple interest for 8 years.
(5) Calculate the amount due if Susan borrowed a sum of $3650 at 8% simple interest for 4 years.
(6) In how much time a principal of $3000 will amount to $3120 at a simple interest of 2% per annum?
(7) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 7% simple interest.
(8) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 8 years.
(9) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 7% simple interest?
(10) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 4 years.