Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 8 years.
Correct Answer
$8692
Solution And Explanation
Solution
Given,
Principal (P) = $5300
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) = $5300 × 8% × 8
= $5300 ×8/100 × 8
= 5300 × 8 × 8/100
= 42400 × 8/100
= 339200/100
= $3392
Thus, Simple Interest = $3392
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 = $5300 + $3392
= $8692
Thus, Amount to be paid = $8692 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 = $5300
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $5300 + ($5300 × 8% × 8)
= $5300 + ($5300 ×8/100 × 8)
= $5300 + (5300 × 8 × 8/100)
= $5300 + (42400 × 8/100)
= $5300 + (339200/100)
= $5300 + $3392 = $8692
Thus, Amount (A) to be paid = $8692 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 $5300, the simple interest in 1 year
= 8/100 × 5300
= 8 × 5300/100
= 42400/100 = $424
Thus, simple interest for 1 year = $424
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $424 × 8 = $3392
Thus, Simple Interest (SI) = $3392
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $3392
= $8692
Thus, Amount to be paid = $8692 Answer
Similar Questions
(1) Thomas took a loan of $5600 at the rate of 8% simple interest per annum. If he paid an amount of $9184 to clear the loan, then find the time period of the loan.
(2) Barbara took a loan of $5100 at the rate of 10% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(3) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $5822 to clear the loan, then find the time period of the loan.
(4) Mary had to pay $3416 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) If Mark paid $5280 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(6) How much loan did Donald borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8125 to clear it?
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 6% simple interest for 7 years.
(8) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 7% simple interest.
(9) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 10% simple interest.