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) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3050 will amount to $3538 at a simple interest of 4% per annum?
(3) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 4 years.
(4) Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 8 years.
(5) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.
(6) Emily had to pay $5177.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) Find the amount to be paid if Richard borrowed a sum of $5600 at 9% simple interest for 8 years.
(8) If Daniel paid $4920 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 2% simple interest for 3 years.
(10) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 2% simple interest.