Question:
Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 7 years.
Correct Answer
$7492.5
Solution And Explanation
Solution
Given,
Principal (P) = $5550
Rate of Simple Interest (SI) = 5%
Time (t) = 7 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) = $5550 × 5% × 7
= $5550 ×5/100 × 7
= 5550 × 5 × 7/100
= 27750 × 7/100
= 194250/100
= $1942.5
Thus, Simple Interest = $1942.5
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 + $1942.5
= $7492.5
Thus, Amount to be paid = $7492.5 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) = 5%
And, Time (t) = 7 years
Thus, Amount (A)
= $5550 + ($5550 × 5% × 7)
= $5550 + ($5550 ×5/100 × 7)
= $5550 + (5550 × 5 × 7/100)
= $5550 + (27750 × 7/100)
= $5550 + (194250/100)
= $5550 + $1942.5 = $7492.5
Thus, Amount (A) to be paid = $7492.5 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 $5550, the simple interest in 1 year
= 5/100 × 5550
= 5 × 5550/100
= 27750/100 = $277.5
Thus, simple interest for 1 year = $277.5
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $277.5 × 7 = $1942.5
Thus, Simple Interest (SI) = $1942.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $1942.5
= $7492.5
Thus, Amount to be paid = $7492.5 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.
(2) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 6% simple interest.
(3) Find the amount to be paid if James borrowed a sum of $5000 at 3% simple interest for 7 years.
(4) Robert had to pay $3379 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 4% simple interest.
(6) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $10164 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 7 years.
(8) Calculate the amount due if Karen borrowed a sum of $3950 at 4% simple interest for 4 years.
(9) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11584 to clear the loan, then find the time period of the loan.
(10) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.