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) If John borrowed $3200 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 5% simple interest for 8 years.
(3) Calculate the amount due if Joseph borrowed a sum of $3700 at 8% simple interest for 3 years.
(4) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 4 years.
(5) Calculate the amount due if Joseph borrowed a sum of $3700 at 9% simple interest for 3 years.
(6) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(7) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $10640 to clear the loan, then find the time period of the loan.
(8) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10452 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 9% simple interest.
(10) How much loan did George borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8760 to clear it?