Question:
Find the amount to be paid if Michael borrowed a sum of $5300 at 9% simple interest for 8 years.
Correct Answer
$9116
Solution And Explanation
Solution
Given,
Principal (P) = $5300
Rate of Simple Interest (SI) = 9%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 8
= $5300 ×9/100 × 8
= 5300 × 9 × 8/100
= 47700 × 8/100
= 381600/100
= $3816
Thus, Simple Interest = $3816
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 + $3816
= $9116
Thus, Amount to be paid = $9116 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) = 9%
And, Time (t) = 8 years
Thus, Amount (A)
= $5300 + ($5300 × 9% × 8)
= $5300 + ($5300 ×9/100 × 8)
= $5300 + (5300 × 9 × 8/100)
= $5300 + (47700 × 8/100)
= $5300 + (381600/100)
= $5300 + $3816 = $9116
Thus, Amount (A) to be paid = $9116 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5300, the simple interest in 1 year
= 9/100 × 5300
= 9 × 5300/100
= 47700/100 = $477
Thus, simple interest for 1 year = $477
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $477 × 8 = $3816
Thus, Simple Interest (SI) = $3816
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5300 + $3816
= $9116
Thus, Amount to be paid = $9116 Answer
Similar Questions
(1) If Kenneth paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?
(3) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 9% simple interest?
(4) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 4 years.
(5) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 4 years.
(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 8 years.
(7) In how much time a principal of $3100 will amount to $3596 at a simple interest of 4% per annum?
(8) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 8% simple interest?
(9) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $9204 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 6% simple interest.