Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.
Correct Answer
$8446
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 8%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 8
= $5150 ×8/100 × 8
= 5150 × 8 × 8/100
= 41200 × 8/100
= 329600/100
= $3296
Thus, Simple Interest = $3296
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 + $3296
= $8446
Thus, Amount to be paid = $8446 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) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $5150 + ($5150 × 8% × 8)
= $5150 + ($5150 ×8/100 × 8)
= $5150 + (5150 × 8 × 8/100)
= $5150 + (41200 × 8/100)
= $5150 + (329600/100)
= $5150 + $3296 = $8446
Thus, Amount (A) to be paid = $8446 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5150, the simple interest in 1 year
= 8/100 × 5150
= 8 × 5150/100
= 41200/100 = $412
Thus, simple interest for 1 year = $412
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $412 × 8 = $3296
Thus, Simple Interest (SI) = $3296
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $3296
= $8446
Thus, Amount to be paid = $8446 Answer
Similar Questions
(1) In how much time a principal of $3200 will amount to $3840 at a simple interest of 5% per annum?
(2) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 10% simple interest?
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 4% simple interest for 4 years.
(4) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 3 years.
(6) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 8% simple interest?
(7) Joshua had to pay $5194 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) William took a loan of $5000 at the rate of 9% simple interest per annum. If he paid an amount of $9500 to clear the loan, then find the time period of the loan.
(9) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.
(10) Christopher had to pay $4480 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.