Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 6% simple interest for 8 years.
Correct Answer
$7622
Solution And Explanation
Solution
Given,
Principal (P) = $5150
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) = $5150 × 6% × 8
= $5150 ×6/100 × 8
= 5150 × 6 × 8/100
= 30900 × 8/100
= 247200/100
= $2472
Thus, Simple Interest = $2472
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 = $5150 + $2472
= $7622
Thus, Amount to be paid = $7622 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 = $5150
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 8 years
Thus, Amount (A)
= $5150 + ($5150 × 6% × 8)
= $5150 + ($5150 ×6/100 × 8)
= $5150 + (5150 × 6 × 8/100)
= $5150 + (30900 × 8/100)
= $5150 + (247200/100)
= $5150 + $2472 = $7622
Thus, Amount (A) to be paid = $7622 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 $5150, the simple interest in 1 year
= 6/100 × 5150
= 6 × 5150/100
= 30900/100 = $309
Thus, simple interest for 1 year = $309
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $309 × 8 = $2472
Thus, Simple Interest (SI) = $2472
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $2472
= $7622
Thus, Amount to be paid = $7622 Answer
Similar Questions
(1) Daniel took a loan of $6200 at the rate of 7% simple interest per annum. If he paid an amount of $10106 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Richard borrowed a sum of $3600 at 3% simple interest for 3 years.
(3) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 2% simple interest?
(4) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $10758 to clear the loan, then find the time period of the loan.
(5) Charles had to pay $4485 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 5% simple interest for 8 years.
(7) Calculate the amount due if William borrowed a sum of $3500 at 2% simple interest for 4 years.
(8) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 10% simple interest?
(9) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.
(10) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 4 years.