Question:
Find the amount to be paid if Barbara borrowed a sum of $5550 at 6% simple interest for 8 years.
Correct Answer
$8214
Solution And Explanation
Solution
Given,
Principal (P) = $5550
Rate of Simple Interest (SI) = 6%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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) = $5550 × 6% × 8
= $5550 ×6/100 × 8
= 5550 × 6 × 8/100
= 33300 × 8/100
= 266400/100
= $2664
Thus, Simple Interest = $2664
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 = $5550 + $2664
= $8214
Thus, Amount to be paid = $8214 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 = $5550
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 8 years
Thus, Amount (A)
= $5550 + ($5550 × 6% × 8)
= $5550 + ($5550 ×6/100 × 8)
= $5550 + (5550 × 6 × 8/100)
= $5550 + (33300 × 8/100)
= $5550 + (266400/100)
= $5550 + $2664 = $8214
Thus, Amount (A) to be paid = $8214 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5550, the simple interest in 1 year
= 6/100 × 5550
= 6 × 5550/100
= 33300/100 = $333
Thus, simple interest for 1 year = $333
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $333 × 8 = $2664
Thus, Simple Interest (SI) = $2664
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $2664
= $8214
Thus, Amount to be paid = $8214 Answer
Similar Questions
(1) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.
(2) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9750 to clear it?
(3) If Michael paid $3564 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(4) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.
(5) If Betty paid $4590 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) If Andrew paid $5376 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(7) How much loan did Jessica borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6325 to clear it?
(8) Lisa had to pay $4414.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Mark took a loan of $6800 at the rate of 9% simple interest per annum. If he paid an amount of $12920 to clear the loan, then find the time period of the loan.
(10) In how much time a principal of $3150 will amount to $3465 at a simple interest of 2% per annum?