Question:
Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 3 years.
Correct Answer
$4779.5
Solution And Explanation
Solution
Given,
Principal (P) = $3950
Rate of Simple Interest (SI) = 7%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $3950 × 7% × 3
= $3950 ×7/100 × 3
= 3950 × 7 × 3/100
= 27650 × 3/100
= 82950/100
= $829.5
Thus, Simple Interest = $829.5
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 = $3950 + $829.5
= $4779.5
Thus, Amount to be paid = $4779.5 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 = $3950
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 3 years
Thus, Amount (A)
= $3950 + ($3950 × 7% × 3)
= $3950 + ($3950 ×7/100 × 3)
= $3950 + (3950 × 7 × 3/100)
= $3950 + (27650 × 3/100)
= $3950 + (82950/100)
= $3950 + $829.5 = $4779.5
Thus, Amount (A) to be paid = $4779.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3950, the simple interest in 1 year
= 7/100 × 3950
= 7 × 3950/100
= 27650/100 = $276.5
Thus, simple interest for 1 year = $276.5
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $276.5 × 3 = $829.5
Thus, Simple Interest (SI) = $829.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3950 + $829.5
= $4779.5
Thus, Amount to be paid = $4779.5 Answer
Similar Questions
(1) In how much time a principal of $3050 will amount to $3294 at a simple interest of 4% per annum?
(2) How much loan did Andrew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8500 to clear it?
(3) Calculate the amount due if Thomas borrowed a sum of $3800 at 8% simple interest for 3 years.
(4) Michael took a loan of $4600 at the rate of 7% simple interest per annum. If he paid an amount of $6532 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 4 years.
(6) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 10% simple interest.
(7) If Steven paid $4968 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) If James paid $3360 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) How much loan did Linda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6687.5 to clear it?
(10) How much loan did Christopher borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6600 to clear it?