Question:
If Robert borrowed $3100 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
Correct Answer
$3286
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 3%
Time (t) = 2 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 2
= $3100 ×3/100 × 2
= 3100 × 3 × 2/100
= 9300 × 2/100
= 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) = 3%
And, Time (t) = 2 years
Thus, Amount (A)
= $3100 + ($3100 × 3% × 2)
= $3100 + ($3100 ×3/100 × 2)
= $3100 + (3100 × 3 × 2/100)
= $3100 + (9300 × 2/100)
= $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 = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $3100, the simple interest in 1 year
= 3/100 × 3100
= 3 × 3100/100
= 9300/100 = $93
Thus, simple interest for 1 year = $93
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $93 × 2 = $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) Calculate the amount due if Christopher borrowed a sum of $4000 at 3% simple interest for 4 years.
(2) Find the amount to be paid if James borrowed a sum of $5000 at 4% simple interest for 8 years.
(3) Find the amount to be paid if Thomas borrowed a sum of $5800 at 10% simple interest for 7 years.
(4) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 9% simple interest?
(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 7 years.
(6) How much loan did Mary borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6060 to clear it?
(7) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.
(8) Sandra took a loan of $6900 at the rate of 7% simple interest per annum. If he paid an amount of $9798 to clear the loan, then find the time period of the loan.
(9) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 4 years.