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) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 2% simple interest.
(2) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 10% simple interest?
(3) Calculate the amount due if Robert borrowed a sum of $3100 at 6% simple interest for 4 years.
(4) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 5% simple interest?
(5) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 3 years.
(6) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(7) Linda had to pay $3852.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(8) Calculate the amount due if Patricia borrowed a sum of $3150 at 7% simple interest for 4 years.
(9) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $9176 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Charles borrowed a sum of $5900 at 9% simple interest for 8 years.