Question:
If Mary borrowed $3050 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
Correct Answer
$3172
Solution And Explanation
Solution
Given,
Principal (P) = $3050
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) = $3050 × 2% × 2
= $3050 ×2/100 × 2
= 3050 × 2 × 2/100
= 6100 × 2/100
= 12200/100
= $122
Thus, Simple Interest = $122
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 = $3050 + $122
= $3172
Thus, Amount to be paid = $3172 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 = $3050
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 2 years
Thus, Amount (A)
= $3050 + ($3050 × 2% × 2)
= $3050 + ($3050 ×2/100 × 2)
= $3050 + (3050 × 2 × 2/100)
= $3050 + (6100 × 2/100)
= $3050 + (12200/100)
= $3050 + $122 = $3172
Thus, Amount (A) to be paid = $3172 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 $3050, the simple interest in 1 year
= 2/100 × 3050
= 2 × 3050/100
= 6100/100 = $61
Thus, simple interest in 1 year = $61
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $61 × 2 = $122
Thus, Simple Interest (SI) = $122
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3050 + $122
= $3172
Thus, Amount to be paid = $3172 Answer
Similar Questions
(1) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $9860 to clear the loan, then find the time period of the loan.
(2) If Thomas paid $4256 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 if Karen borrowed a sum of $3950 at 6% simple interest for 3 years.
(4) Linda took a loan of $4700 at the rate of 9% simple interest per annum. If he paid an amount of $8084 to clear the loan, then find the time period of the loan.
(5) If Joseph paid $4440 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) Elizabeth had to pay $3864 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 10% simple interest?
(8) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 7 years.
(9) If David borrowed $3400 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(10) If Margaret paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.