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) 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.
(2) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $8932 to clear the loan, then find the time period of the loan.
(3) Mark took a loan of $6800 at the rate of 8% simple interest per annum. If he paid an amount of $12240 to clear the loan, then find the time period of the loan.
(4) If Elizabeth paid $3726 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 7% simple interest?
(6) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?
(7) Calculate the amount due if David borrowed a sum of $3400 at 7% simple interest for 3 years.
(8) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 10% simple interest?
(9) Mark had to pay $4796 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(10) 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?