Question:
What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 9% simple interest?
Correct Answer
$4422.5
Solution And Explanation
Solution
Given,
Principal (P) = $3050
Rate of Simple Interest (SI) = 9%
Time (t) = 5 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) = $3050 × 9% × 5
= $3050 ×9/100 × 5
= 3050 × 9 × 5/100
= 27450 × 5/100
= 137250/100
= $1372.5
Thus, Simple Interest = $1372.5
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 = $3050 + $1372.5
= $4422.5
Thus, Amount to be paid = $4422.5 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 = $3050
Rate of Simple Interest (SI) or (R) = 9%
And, Time (t) = 5 years
Thus, Amount (A)
= $3050 + ($3050 × 9% × 5)
= $3050 + ($3050 ×9/100 × 5)
= $3050 + (3050 × 9 × 5/100)
= $3050 + (27450 × 5/100)
= $3050 + (137250/100)
= $3050 + $1372.5 = $4422.5
Thus, Amount (A) to be paid = $4422.5 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 $3050, the simple interest in 1 year
= 9/100 × 3050
= 9 × 3050/100
= 27450/100 = $274.5
Thus, simple interest for 1 year = $274.5
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $274.5 × 5 = $1372.5
Thus, Simple Interest (SI) = $1372.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3050 + $1372.5
= $4422.5
Thus, Amount to be paid = $4422.5 Answer
Similar Questions
(1) If Michelle paid $5346 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) Elizabeth took a loan of $4900 at the rate of 6% simple interest per annum. If he paid an amount of $6664 to clear the loan, then find the time period of the loan.
(3) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 10% simple interest?
(4) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 3% simple interest?
(5) Karen took a loan of $5900 at the rate of 9% simple interest per annum. If he paid an amount of $10679 to clear the loan, then find the time period of the loan.
(6) Ashley had to pay $5096 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9437.5 to clear it?
(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 8% simple interest for 7 years.
(9) Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 10% simple interest.
(10) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $8640 to clear the loan, then find the time period of the loan.