Question:
Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 3 years.
Correct Answer
$4197.5
Solution And Explanation
Solution
Given,
Principal (P) = $3650
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) = $3650 × 5% × 3
= $3650 ×5/100 × 3
= 3650 × 5 × 3/100
= 18250 × 3/100
= 54750/100
= $547.5
Thus, Simple Interest = $547.5
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 = $3650 + $547.5
= $4197.5
Thus, Amount to be paid = $4197.5 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 = $3650
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 3 years
Thus, Amount (A)
= $3650 + ($3650 × 5% × 3)
= $3650 + ($3650 ×5/100 × 3)
= $3650 + (3650 × 5 × 3/100)
= $3650 + (18250 × 3/100)
= $3650 + (54750/100)
= $3650 + $547.5 = $4197.5
Thus, Amount (A) to be paid = $4197.5 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 $3650, the simple interest in 1 year
= 5/100 × 3650
= 5 × 3650/100
= 18250/100 = $182.5
Thus, simple interest for 1 year = $182.5
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $182.5 × 3 = $547.5
Thus, Simple Interest (SI) = $547.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3650 + $547.5
= $4197.5
Thus, Amount to be paid = $4197.5 Answer
Similar Questions
(1) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 10% simple interest.
(2) Calculate the amount due if Charles borrowed a sum of $3900 at 10% simple interest for 4 years.
(3) How much loan did Karen borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7140 to clear it?
(4) Find the amount to be paid if Patricia borrowed a sum of $5150 at 4% simple interest for 7 years.
(5) Calculate the amount due if James borrowed a sum of $3000 at 6% simple interest for 4 years.
(6) In how much time a principal of $3200 will amount to $3456 at a simple interest of 4% per annum?
(7) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.
(8) Margaret had to pay $5002.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 6% simple interest for 8 years.