Question:
Calculate the amount due if Barbara borrowed a sum of $3550 at 5% simple interest for 4 years.
Correct Answer
$4260
Solution And Explanation
Solution
Given,
Principal (P) = $3550
Rate of Simple Interest (SI) = 5%
Time (t) = 4 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% × 4
= $3550 ×5/100 × 4
= 3550 × 5 × 4/100
= 17750 × 4/100
= 71000/100
= $710
Thus, Simple Interest = $710
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 + $710
= $4260
Thus, Amount to be paid = $4260 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) = 4 years
Thus, Amount (A)
= $3550 + ($3550 × 5% × 4)
= $3550 + ($3550 ×5/100 × 4)
= $3550 + (3550 × 5 × 4/100)
= $3550 + (17750 × 4/100)
= $3550 + (71000/100)
= $3550 + $710 = $4260
Thus, Amount (A) to be paid = $4260 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 4 years
= Simple interest for 1 year × 4
= $177.5 × 4 = $710
Thus, Simple Interest (SI) = $710
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3550 + $710
= $4260
Thus, Amount to be paid = $4260 Answer
Similar Questions
(1) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
(2) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.
(3) Mark took a loan of $6800 at the rate of 10% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 8 years.
(5) Charles took a loan of $5800 at the rate of 8% simple interest per annum. If he paid an amount of $8584 to clear the loan, then find the time period of the loan.
(6) If Anthony paid $4988 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Michael had to pay $3498 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 8 years.
(9) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 9% simple interest.
(10) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 3 years.