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) How much loan did Nancy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7072.5 to clear it?
(2) If Sarah borrowed $3850 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(3) Matthew had to pay $4830 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.
(5) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 9% simple interest.
(6) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $9200 to clear the loan, then find the time period of the loan.
(7) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7980 to clear it?
(8) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(9) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.
(10) In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?