Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 7 years.
Correct Answer
$6952.5
Solution And Explanation
Solution
Given,
Principal (P) = $5150
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) = $5150 × 5% × 7
= $5150 ×5/100 × 7
= 5150 × 5 × 7/100
= 25750 × 7/100
= 180250/100
= $1802.5
Thus, Simple Interest = $1802.5
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 = $5150 + $1802.5
= $6952.5
Thus, Amount to be paid = $6952.5 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 = $5150
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 7 years
Thus, Amount (A)
= $5150 + ($5150 × 5% × 7)
= $5150 + ($5150 ×5/100 × 7)
= $5150 + (5150 × 5 × 7/100)
= $5150 + (25750 × 7/100)
= $5150 + (180250/100)
= $5150 + $1802.5 = $6952.5
Thus, Amount (A) to be paid = $6952.5 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 $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 7 years
= Simple interest for 1 year × 7
= $257.5 × 7 = $1802.5
Thus, Simple Interest (SI) = $1802.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $1802.5
= $6952.5
Thus, Amount to be paid = $6952.5 Answer
Similar Questions
(1) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 8 years.
(2) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 8 years.
(3) In how much time a principal of $3050 will amount to $3294 at a simple interest of 2% per annum?
(4) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 8 years.
(6) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 8% simple interest?
(7) What amount will be due after 2 years if Steven borrowed a sum of $3800 at a 8% simple interest?
(8) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 2% simple interest for 7 years.
(9) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 3% simple interest.
(10) Jessica took a loan of $5500 at the rate of 8% simple interest per annum. If he paid an amount of $9020 to clear the loan, then find the time period of the loan.