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) How much loan did Mary borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6060 to clear it?
(2) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $8364 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.
(4) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.
(5) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(6) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $9000 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Susan borrowed a sum of $5650 at a rate of 4% simple interest.
(8) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $8840 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.
(10) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 3 years.