Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 8 years.
Correct Answer
$7210
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 5%
Time (t) = 8 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) = $5150 × 5% × 8
= $5150 ×5/100 × 8
= 5150 × 5 × 8/100
= 25750 × 8/100
= 206000/100
= $2060
Thus, Simple Interest = $2060
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 + $2060
= $7210
Thus, Amount to be paid = $7210 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) = 5%
And, Time (t) = 8 years
Thus, Amount (A)
= $5150 + ($5150 × 5% × 8)
= $5150 + ($5150 ×5/100 × 8)
= $5150 + (5150 × 5 × 8/100)
= $5150 + (25750 × 8/100)
= $5150 + (206000/100)
= $5150 + $2060 = $7210
Thus, Amount (A) to be paid = $7210 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 $5150, the simple interest in 1 year
= 5/100 × 5150
= 5 × 5150/100
= 25750/100 = $257.5
Thus, simple interest for 1 year = $257.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $257.5 × 8 = $2060
Thus, Simple Interest (SI) = $2060
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $2060
= $7210
Thus, Amount to be paid = $7210 Answer
Similar Questions
(1) Find the amount to be paid if Joseph borrowed a sum of $5700 at 9% simple interest for 8 years.
(2) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.
(3) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $8296 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if William borrowed a sum of $5500 at 6% simple interest for 8 years.
(5) Joseph had to pay $3922 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $7450 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 3 years.
(8) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Joseph borrowed a sum of $3700 at 5% simple interest for 3 years.
(10) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6109 to clear the loan, then find the time period of the loan.