Question:
If Michael borrowed $3300 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
Correct Answer
$3498
Solution And Explanation
Solution
Given,
Principal (P) = $3300
Rate of Simple Interest (SI) = 3%
Time (t) = 2 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 2
= $3300 ×3/100 × 2
= 3300 × 3 × 2/100
= 9900 × 2/100
= 19800/100
= $198
Thus, Simple Interest = $198
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 + $198
= $3498
Thus, Amount to be paid = $3498 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) = 3%
And, Time (t) = 2 years
Thus, Amount (A)
= $3300 + ($3300 × 3% × 2)
= $3300 + ($3300 ×3/100 × 2)
= $3300 + (3300 × 3 × 2/100)
= $3300 + (9900 × 2/100)
= $3300 + (19800/100)
= $3300 + $198 = $3498
Thus, Amount (A) to be paid = $3498 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $3300, the simple interest in 1 year
= 3/100 × 3300
= 3 × 3300/100
= 9900/100 = $99
Thus, simple interest for 1 year = $99
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $99 × 2 = $198
Thus, Simple Interest (SI) = $198
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3300 + $198
= $3498
Thus, Amount to be paid = $3498 Answer
Similar Questions
(1) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 10% simple interest?
(2) Betty took a loan of $6500 at the rate of 6% simple interest per annum. If he paid an amount of $10010 to clear the loan, then find the time period of the loan.
(3) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5680 to clear the loan, then find the time period of the loan.
(4) In how much time a principal of $3150 will amount to $3780 at a simple interest of 4% per annum?
(5) Susan took a loan of $5300 at the rate of 6% simple interest per annum. If he paid an amount of $8162 to clear the loan, then find the time period of the loan.
(6) In how much time a principal of $3100 will amount to $3224 at a simple interest of 2% per annum?
(7) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 2% simple interest?
(8) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $9089 to clear the loan, then find the time period of the loan.
(9) Kenneth had to pay $5300 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 5% simple interest for 8 years.