Question:
If James borrowed $3000 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
Correct Answer
$3180
Solution And Explanation
Solution
Given,
Principal (P) = $3000
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) = $3000 × 3% × 2
= $3000 ×3/100 × 2
= 3000 × 3 × 2/100
= 9000 × 2/100
= 18000/100
= $180
Thus, Simple Interest = $180
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 = $3000 + $180
= $3180
Thus, Amount to be paid = $3180 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 = $3000
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 2 years
Thus, Amount (A)
= $3000 + ($3000 × 3% × 2)
= $3000 + ($3000 ×3/100 × 2)
= $3000 + (3000 × 3 × 2/100)
= $3000 + (9000 × 2/100)
= $3000 + (18000/100)
= $3000 + $180 = $3180
Thus, Amount (A) to be paid = $3180 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 $3000, the simple interest in 1 year
= 3/100 × 3000
= 3 × 3000/100
= 9000/100 = $90
Thus, simple interest for 1 year = $90
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $90 × 2 = $180
Thus, Simple Interest (SI) = $180
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3000 + $180
= $3180
Thus, Amount to be paid = $3180 Answer
Similar Questions
(1) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 2% simple interest?
(2) How much loan did Kenneth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8400 to clear it?
(3) How much loan did Kevin borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7810 to clear it?
(4) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 7% simple interest.
(6) David had to pay $3808 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 4 years.
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 6% simple interest for 7 years.
(9) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 6% simple interest for 7 years.
(10) In how much time a principal of $3200 will amount to $3520 at a simple interest of 2% per annum?