Question:
Find the amount to be paid if Barbara borrowed a sum of $5550 at 8% simple interest for 7 years.
Correct Answer
$8658
Solution And Explanation
Solution
Given,
Principal (P) = $5550
Rate of Simple Interest (SI) = 8%
Time (t) = 7 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 7
= $5550 ×8/100 × 7
= 5550 × 8 × 7/100
= 44400 × 7/100
= 310800/100
= $3108
Thus, Simple Interest = $3108
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 + $3108
= $8658
Thus, Amount to be paid = $8658 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) = 8%
And, Time (t) = 7 years
Thus, Amount (A)
= $5550 + ($5550 × 8% × 7)
= $5550 + ($5550 ×8/100 × 7)
= $5550 + (5550 × 8 × 7/100)
= $5550 + (44400 × 7/100)
= $5550 + (310800/100)
= $5550 + $3108 = $8658
Thus, Amount (A) to be paid = $8658 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5550, the simple interest in 1 year
= 8/100 × 5550
= 8 × 5550/100
= 44400/100 = $444
Thus, simple interest for 1 year = $444
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $444 × 7 = $3108
Thus, Simple Interest (SI) = $3108
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $3108
= $8658
Thus, Amount to be paid = $8658 Answer
Similar Questions
(1) If Mark paid $4752 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(3) Jessica had to pay $4087.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) Find the amount to be paid if Michael borrowed a sum of $5300 at 7% simple interest for 8 years.
(5) In how much time a principal of $3150 will amount to $3402 at a simple interest of 2% per annum?
(6) How much loan did Linda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6687.5 to clear it?
(7) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9437.5 to clear it?
(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 2% simple interest for 8 years.
(9) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 4 years.