Question:
Calculate the amount due if Mary borrowed a sum of $3050 at 5% simple interest for 3 years.
Correct Answer
$3507.5
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (SI) = 5%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 3
= $3050 ×5/100 × 3
= 3050 × 5 × 3/100
= 15250 × 3/100
= 45750/100
= $457.5
Thus, Simple Interest = $457.5
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 + $457.5
= $3507.5
Thus, Amount to be paid = $3507.5 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) = 5%
And, Time (t) = 3 years
Thus, Amount (A)
= $3050 + ($3050 × 5% × 3)
= $3050 + ($3050 ×5/100 × 3)
= $3050 + (3050 × 5 × 3/100)
= $3050 + (15250 × 3/100)
= $3050 + (45750/100)
= $3050 + $457.5 = $3507.5
Thus, Amount (A) to be paid = $3507.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3050, the simple interest in 1 year
= 5/100 × 3050
= 5 × 3050/100
= 15250/100 = $152.5
Thus, simple interest for 1 year = $152.5
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $152.5 × 3 = $457.5
Thus, Simple Interest (SI) = $457.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3050 + $457.5
= $3507.5
Thus, Amount to be paid = $3507.5 Answer
Similar Questions
(1) Sarah took a loan of $5700 at the rate of 7% simple interest per annum. If he paid an amount of $8094 to clear the loan, then find the time period of the loan.
(2) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9360 to clear it?
(3) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 2% simple interest.
(5) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.
(6) How much loan did Jessica borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6612.5 to clear it?
(7) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 3 years.
(8) If Michael paid $3828 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 7 years.
(10) If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.