Question:
Calculate the amount due if Michael borrowed a sum of $3300 at 5% simple interest for 3 years.
Correct Answer
$3795
Solution And Explanation
Solution
Given,
Principal (P) = $3300
Rate of Simple Interest (SI) = 5%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 3
= $3300 ×5/100 × 3
= 3300 × 5 × 3/100
= 16500 × 3/100
= 49500/100
= $495
Thus, Simple Interest = $495
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 + $495
= $3795
Thus, Amount to be paid = $3795 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) = 5%
And, Time (t) = 3 years
Thus, Amount (A)
= $3300 + ($3300 × 5% × 3)
= $3300 + ($3300 ×5/100 × 3)
= $3300 + (3300 × 5 × 3/100)
= $3300 + (16500 × 3/100)
= $3300 + (49500/100)
= $3300 + $495 = $3795
Thus, Amount (A) to be paid = $3795 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3300, the simple interest in 1 year
= 5/100 × 3300
= 5 × 3300/100
= 16500/100 = $165
Thus, simple interest for 1 year = $165
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $165 × 3 = $495
Thus, Simple Interest (SI) = $495
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3300 + $495
= $3795
Thus, Amount to be paid = $3795 Answer
Similar Questions
(1) If Richard paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 7% simple interest for 8 years.
(4) How much loan did Jessica borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6325 to clear it?
(5) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 2% simple interest?
(6) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 2% simple interest.
(7) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.
(8) In how much time a principal of $3100 will amount to $3379 at a simple interest of 3% per annum?
(9) In how much time a principal of $3000 will amount to $3450 at a simple interest of 5% per annum?
(10) What amount does Charles have to pay after 6 years if he takes a loan of $3900 at 6% simple interest?