Question:
What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 10% simple interest?
Correct Answer
$4950
Solution And Explanation
Solution
Given,
Principal (P) = $3300
Rate of Simple Interest (SI) = 10%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 5
= $3300 ×10/100 × 5
= 3300 × 10 × 5/100
= 33000 × 5/100
= 165000/100
= $1650
Thus, Simple Interest = $1650
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 + $1650
= $4950
Thus, Amount to be paid = $4950 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) = 10%
And, Time (t) = 5 years
Thus, Amount (A)
= $3300 + ($3300 × 10% × 5)
= $3300 + ($3300 ×10/100 × 5)
= $3300 + (3300 × 10 × 5/100)
= $3300 + (33000 × 5/100)
= $3300 + (165000/100)
= $3300 + $1650 = $4950
Thus, Amount (A) to be paid = $4950 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3300, the simple interest in 1 year
= 10/100 × 3300
= 10 × 3300/100
= 33000/100 = $330
Thus, simple interest for 1 year = $330
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $330 × 5 = $1650
Thus, Simple Interest (SI) = $1650
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3300 + $1650
= $4950
Thus, Amount to be paid = $4950 Answer
Similar Questions
(1) Calculate the amount due if Richard borrowed a sum of $3600 at 10% simple interest for 3 years.
(2) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $10000 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Charles borrowed a sum of $3450 at a 5% simple interest?
(4) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 8 years.
(5) Find the amount to be paid if Barbara borrowed a sum of $5550 at 2% simple interest for 8 years.
(6) Elizabeth took a loan of $4900 at the rate of 9% simple interest per annum. If he paid an amount of $9310 to clear the loan, then find the time period of the loan.
(7) Barbara had to pay $3763 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(8) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 7 years.
(9) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 8 years.
(10) How much loan did Brian borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9000 to clear it?