Question:
Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 3 years.
Correct Answer
$4082.5
Solution And Explanation
Solution
Given,
Principal (P) = $3550
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) = $3550 × 5% × 3
= $3550 ×5/100 × 3
= 3550 × 5 × 3/100
= 17750 × 3/100
= 53250/100
= $532.5
Thus, Simple Interest = $532.5
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 = $3550 + $532.5
= $4082.5
Thus, Amount to be paid = $4082.5 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 = $3550
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 3 years
Thus, Amount (A)
= $3550 + ($3550 × 5% × 3)
= $3550 + ($3550 ×5/100 × 3)
= $3550 + (3550 × 5 × 3/100)
= $3550 + (17750 × 3/100)
= $3550 + (53250/100)
= $3550 + $532.5 = $4082.5
Thus, Amount (A) to be paid = $4082.5 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 $3550, the simple interest in 1 year
= 5/100 × 3550
= 5 × 3550/100
= 17750/100 = $177.5
Thus, simple interest for 1 year = $177.5
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $177.5 × 3 = $532.5
Thus, Simple Interest (SI) = $532.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3550 + $532.5
= $4082.5
Thus, Amount to be paid = $4082.5 Answer
Similar Questions
(1) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 8 years.
(2) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 4 years.
(3) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.
(4) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 8 years.
(5) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12800 to clear the loan, then find the time period of the loan.
(6) How much loan did Mark borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7680 to clear it?
(7) How much loan did Matthew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7440 to clear it?
(8) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.
(9) Michelle had to pay $5544 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(10) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 7% simple interest?