Question:
Calculate the amount due if Barbara borrowed a sum of $3550 at 10% simple interest for 3 years.
Correct Answer
$4615
Solution And Explanation
Solution
Given,
Principal (P) = $3550
Rate of Simple Interest (SI) = 10%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 3
= $3550 ×10/100 × 3
= 3550 × 10 × 3/100
= 35500 × 3/100
= 106500/100
= $1065
Thus, Simple Interest = $1065
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 + $1065
= $4615
Thus, Amount to be paid = $4615 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) = 10%
And, Time (t) = 3 years
Thus, Amount (A)
= $3550 + ($3550 × 10% × 3)
= $3550 + ($3550 ×10/100 × 3)
= $3550 + (3550 × 10 × 3/100)
= $3550 + (35500 × 3/100)
= $3550 + (106500/100)
= $3550 + $1065 = $4615
Thus, Amount (A) to be paid = $4615 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3550, the simple interest in 1 year
= 10/100 × 3550
= 10 × 3550/100
= 35500/100 = $355
Thus, simple interest for 1 year = $355
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $355 × 3 = $1065
Thus, Simple Interest (SI) = $1065
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3550 + $1065
= $4615
Thus, Amount to be paid = $4615 Answer
Similar Questions
(1) What amount does David have to pay after 5 years if he takes a loan of $3400 at 5% simple interest?
(2) Richard took a loan of $5200 at the rate of 9% simple interest per annum. If he paid an amount of $8476 to clear the loan, then find the time period of the loan.
(3) Christopher had to pay $4600 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
(5) If Donald paid $5040 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(6) Donna had to pay $5286.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 4 years.
(9) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $6936 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 7 years.