Question:
Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 3 years.
Correct Answer
$3416
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (SI) = 4%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 3
= $3050 ×4/100 × 3
= 3050 × 4 × 3/100
= 12200 × 3/100
= 36600/100
= $366
Thus, Simple Interest = $366
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 + $366
= $3416
Thus, Amount to be paid = $3416 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) = 4%
And, Time (t) = 3 years
Thus, Amount (A)
= $3050 + ($3050 × 4% × 3)
= $3050 + ($3050 ×4/100 × 3)
= $3050 + (3050 × 4 × 3/100)
= $3050 + (12200 × 3/100)
= $3050 + (36600/100)
= $3050 + $366 = $3416
Thus, Amount (A) to be paid = $3416 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $3050, the simple interest in 1 year
= 4/100 × 3050
= 4 × 3050/100
= 12200/100 = $122
Thus, simple interest for 1 year = $122
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $122 × 3 = $366
Thus, Simple Interest (SI) = $366
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3050 + $366
= $3416
Thus, Amount to be paid = $3416 Answer
Similar Questions
(1) Mary took a loan of $4100 at the rate of 10% simple interest per annum. If he paid an amount of $7380 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.
(3) Jessica took a loan of $5500 at the rate of 7% simple interest per annum. If he paid an amount of $8580 to clear the loan, then find the time period of the loan.
(4) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 4% simple interest.
(6) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $7052 to clear the loan, then find the time period of the loan.
(7) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8892 to clear the loan, then find the time period of the loan.
(8) How much loan did Jacob borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $9200 to clear it?
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 8 years.
(10) In how much time a principal of $3150 will amount to $3402 at a simple interest of 4% per annum?