Question:
What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 5% simple interest?
Correct Answer
$5200
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (SI) = 5%
Time (t) = 6 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) = $4000 × 5% × 6
= $4000 ×5/100 × 6
= 4000 × 5 × 6/100
= 20000 × 6/100
= 120000/100
= $1200
Thus, Simple Interest = $1200
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 = $4000 + $1200
= $5200
Thus, Amount to be paid = $5200 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 = $4000
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 6 years
Thus, Amount (A)
= $4000 + ($4000 × 5% × 6)
= $4000 + ($4000 ×5/100 × 6)
= $4000 + (4000 × 5 × 6/100)
= $4000 + (20000 × 6/100)
= $4000 + (120000/100)
= $4000 + $1200 = $5200
Thus, Amount (A) to be paid = $5200 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 $4000, the simple interest in 1 year
= 5/100 × 4000
= 5 × 4000/100
= 20000/100 = $200
Thus, simple interest for 1 year = $200
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $200 × 6 = $1200
Thus, Simple Interest (SI) = $1200
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $4000 + $1200
= $5200
Thus, Amount to be paid = $5200 Answer
Similar Questions
(1) Find the amount to be paid if Christopher borrowed a sum of $6000 at 7% simple interest for 8 years.
(2) Michael had to pay $3696 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 4 years.
(4) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 6% simple interest?
(5) Karen took a loan of $5900 at the rate of 10% simple interest per annum. If he paid an amount of $11800 to clear the loan, then find the time period of the loan.
(6) Jessica took a loan of $5500 at the rate of 9% simple interest per annum. If he paid an amount of $9955 to clear the loan, then find the time period of the loan.
(7) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $7310 to clear the loan, then find the time period of the loan.
(8) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 7% simple interest?
(9) What amount will be due after 2 years if John borrowed a sum of $3100 at a 5% simple interest?
(10) What amount does William have to pay after 6 years if he takes a loan of $3500 at 8% simple interest?