Question:
What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 5% simple interest?
Correct Answer
$4615
Solution And Explanation
Solution
Given,
Principal (P) = $3550
Rate of Simple Interest (SI) = 5%
Time (t) = 6 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% × 6
= $3550 ×5/100 × 6
= 3550 × 5 × 6/100
= 17750 × 6/100
= 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) = 5%
And, Time (t) = 6 years
Thus, Amount (A)
= $3550 + ($3550 × 5% × 6)
= $3550 + ($3550 ×5/100 × 6)
= $3550 + (3550 × 5 × 6/100)
= $3550 + (17750 × 6/100)
= $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 = 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 6 years
= Simple interest for 1 year × 6
= $177.5 × 6 = $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) How much loan did Andrew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8500 to clear it?
(2) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.
(3) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $13200 to clear the loan, then find the time period of the loan.
(4) Sarah took a loan of $5700 at the rate of 8% simple interest per annum. If he paid an amount of $8436 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 8 years.
(6) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 8 years.
(7) Calculate the amount due if James borrowed a sum of $3000 at 9% simple interest for 3 years.
(8) If Charles paid $4212 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) If Michael paid $3960 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(10) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 3% simple interest for 8 years.