Question:
What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 9% simple interest?
Correct Answer
$5082
Solution And Explanation
Solution
Given,
Principal (P) = $3300
Rate of Simple Interest (SI) = 9%
Time (t) = 6 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) = $3300 × 9% × 6
= $3300 ×9/100 × 6
= 3300 × 9 × 6/100
= 29700 × 6/100
= 178200/100
= $1782
Thus, Simple Interest = $1782
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 = $3300 + $1782
= $5082
Thus, Amount to be paid = $5082 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 = $3300
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 6 years
Thus, Amount (A)
= $3300 + ($3300 × 9% × 6)
= $3300 + ($3300 ×9/100 × 6)
= $3300 + (3300 × 9 × 6/100)
= $3300 + (29700 × 6/100)
= $3300 + (178200/100)
= $3300 + $1782 = $5082
Thus, Amount (A) to be paid = $5082 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 $3300, the simple interest in 1 year
= 9/100 × 3300
= 9 × 3300/100
= 29700/100 = $297
Thus, simple interest for 1 year = $297
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $297 × 6 = $1782
Thus, Simple Interest (SI) = $1782
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3300 + $1782
= $5082
Thus, Amount to be paid = $5082 Answer
Similar Questions
(1) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 5% simple interest?
(2) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 3% simple interest for 4 years.
(4) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 7 years.
(5) Elizabeth had to pay $3657 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Elizabeth had to pay $3760.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) How much loan did Matthew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7750 to clear it?
(8) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.
(9) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 10% simple interest.