Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 8 years.
Correct Answer
$9270
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 10%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 8
= $5150 ×10/100 × 8
= 5150 × 10 × 8/100
= 51500 × 8/100
= 412000/100
= $4120
Thus, Simple Interest = $4120
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 + $4120
= $9270
Thus, Amount to be paid = $9270 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) = 10%
And, Time (t) = 8 years
Thus, Amount (A)
= $5150 + ($5150 × 10% × 8)
= $5150 + ($5150 ×10/100 × 8)
= $5150 + (5150 × 10 × 8/100)
= $5150 + (51500 × 8/100)
= $5150 + (412000/100)
= $5150 + $4120 = $9270
Thus, Amount (A) to be paid = $9270 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $5150, the simple interest in 1 year
= 10/100 × 5150
= 10 × 5150/100
= 51500/100 = $515
Thus, simple interest for 1 year = $515
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $515 × 8 = $4120
Thus, Simple Interest (SI) = $4120
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $4120
= $9270
Thus, Amount to be paid = $9270 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.
(2) Find the amount to be paid if Sarah borrowed a sum of $5850 at 6% simple interest for 7 years.
(3) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 7 years.
(4) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 8% simple interest.
(5) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12800 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 8% simple interest.
(7) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $9840 to clear the loan, then find the time period of the loan.
(8) What amount does David have to pay after 6 years if he takes a loan of $3400 at 5% simple interest?
(9) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 3 years.
(10) Find the amount to be paid if Mary borrowed a sum of $5050 at 8% simple interest for 7 years.