Question:
Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 3 years.
Correct Answer
$3869.5
Solution And Explanation
Solution
Given,
Principal (P) = $3550
Rate of Simple Interest (SI) = 3%
Time (t) = 3 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) = $3550 × 3% × 3
= $3550 ×3/100 × 3
= 3550 × 3 × 3/100
= 10650 × 3/100
= 31950/100
= $319.5
Thus, Simple Interest = $319.5
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 + $319.5
= $3869.5
Thus, Amount to be paid = $3869.5 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) = 3%
And, Time (t) = 3 years
Thus, Amount (A)
= $3550 + ($3550 × 3% × 3)
= $3550 + ($3550 ×3/100 × 3)
= $3550 + (3550 × 3 × 3/100)
= $3550 + (10650 × 3/100)
= $3550 + (31950/100)
= $3550 + $319.5 = $3869.5
Thus, Amount (A) to be paid = $3869.5 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 $3550, the simple interest in 1 year
= 3/100 × 3550
= 3 × 3550/100
= 10650/100 = $106.5
Thus, simple interest for 1 year = $106.5
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $106.5 × 3 = $319.5
Thus, Simple Interest (SI) = $319.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3550 + $319.5
= $3869.5
Thus, Amount to be paid = $3869.5 Answer
Similar Questions
(1) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 4 years.
(2) William took a loan of $5000 at the rate of 8% simple interest per annum. If he paid an amount of $7400 to clear the loan, then find the time period of the loan.
(3) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.
(4) If Donna paid $5432 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(5) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $10432 to clear the loan, then find the time period of the loan.
(6) How much loan did Ronald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8625 to clear it?
(7) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 4% simple interest.
(8) Barbara had to pay $3869.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7224 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 4% simple interest.