Question:
If Robert borrowed $3100 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
Correct Answer
$3224
Solution And Explanation
Solution
Given,
Principal (P) = $3100
Rate of Simple Interest (SI) = 2%
Time (t) = 2 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% × 2
= $3100 ×2/100 × 2
= 3100 × 2 × 2/100
= 6200 × 2/100
= 12400/100
= $124
Thus, Simple Interest = $124
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 + $124
= $3224
Thus, Amount to be paid = $3224 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) = 2 years
Thus, Amount (A)
= $3100 + ($3100 × 2% × 2)
= $3100 + ($3100 ×2/100 × 2)
= $3100 + (3100 × 2 × 2/100)
= $3100 + (6200 × 2/100)
= $3100 + (12400/100)
= $3100 + $124 = $3224
Thus, Amount (A) to be paid = $3224 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 in 1 year = $2
∴ For $1, the simple interest in 1 year = 2/100
∴ For $3100, the simple interest in 1 year
= 2/100 × 3100
= 2 × 3100/100
= 6200/100 = $62
Thus, simple interest in 1 year = $62
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $62 × 2 = $124
Thus, Simple Interest (SI) = $124
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3100 + $124
= $3224
Thus, Amount to be paid = $3224 Answer
Similar Questions
(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 7% simple interest for 8 years.
(2) If Jennifer paid $3640 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 3% simple interest.
(4) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
(5) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
(6) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 9% simple interest?
(7) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $10496 to clear the loan, then find the time period of the loan.
(8) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $7480 to clear the loan, then find the time period of the loan.
(9) In how much time a principal of $3050 will amount to $3233 at a simple interest of 2% per annum?
(10) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 5% simple interest.