Question:
If Patricia borrowed $3150 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
Correct Answer
$3339
Solution And Explanation
Solution
Given,
Principal (P) = $3150
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) = $3150 × 3% × 2
= $3150 ×3/100 × 2
= 3150 × 3 × 2/100
= 9450 × 2/100
= 18900/100
= $189
Thus, Simple Interest = $189
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 = $3150 + $189
= $3339
Thus, Amount to be paid = $3339 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 = $3150
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 2 years
Thus, Amount (A)
= $3150 + ($3150 × 3% × 2)
= $3150 + ($3150 ×3/100 × 2)
= $3150 + (3150 × 3 × 2/100)
= $3150 + (9450 × 2/100)
= $3150 + (18900/100)
= $3150 + $189 = $3339
Thus, Amount (A) to be paid = $3339 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 $3150, the simple interest in 1 year
= 3/100 × 3150
= 3 × 3150/100
= 9450/100 = $94.5
Thus, simple interest for 1 year = $94.5
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $94.5 × 2 = $189
Thus, Simple Interest (SI) = $189
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $189
= $3339
Thus, Amount to be paid = $3339 Answer
Similar Questions
(1) Calculate the amount due if Jessica borrowed a sum of $3750 at 5% simple interest for 3 years.
(2) How much loan did Joshua borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8280 to clear it?
(3) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(4) Linda took a loan of $4700 at the rate of 10% simple interest per annum. If he paid an amount of $9400 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 8% simple interest.
(6) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 3% simple interest?
(7) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8008 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Michael borrowed a sum of $3300 at 10% simple interest for 4 years.
(9) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.
(10) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 4% simple interest?