Question:
Calculate the amount due if Karen borrowed a sum of $3950 at 5% simple interest for 4 years.
Correct Answer
$4740
Solution And Explanation
Solution
Given,
Principal (P) = $3950
Rate of Simple Interest (SI) = 5%
Time (t) = 4 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) = $3950 × 5% × 4
= $3950 ×5/100 × 4
= 3950 × 5 × 4/100
= 19750 × 4/100
= 79000/100
= $790
Thus, Simple Interest = $790
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 + $790
= $4740
Thus, Amount to be paid = $4740 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) = 5%
And, Time (t) = 4 years
Thus, Amount (A)
= $3950 + ($3950 × 5% × 4)
= $3950 + ($3950 ×5/100 × 4)
= $3950 + (3950 × 5 × 4/100)
= $3950 + (19750 × 4/100)
= $3950 + (79000/100)
= $3950 + $790 = $4740
Thus, Amount (A) to be paid = $4740 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 $3950, the simple interest in 1 year
= 5/100 × 3950
= 5 × 3950/100
= 19750/100 = $197.5
Thus, simple interest for 1 year = $197.5
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $197.5 × 4 = $790
Thus, Simple Interest (SI) = $790
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3950 + $790
= $4740
Thus, Amount to be paid = $4740 Answer
Similar Questions
(1) Joseph took a loan of $5400 at the rate of 9% simple interest per annum. If he paid an amount of $9774 to clear the loan, then find the time period of the loan.
(2) How much loan did Sarah borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6727.5 to clear it?
(3) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $11780 to clear the loan, then find the time period of the loan.
(4) Matthew took a loan of $6400 at the rate of 9% simple interest per annum. If he paid an amount of $11584 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 5% simple interest?
(6) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8432 to clear the loan, then find the time period of the loan.
(7) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10320 to clear the loan, then find the time period of the loan.
(8) What amount does William have to pay after 6 years if he takes a loan of $3500 at 6% simple interest?
(9) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6106 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 2% simple interest for 8 years.