Question:
What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 10% simple interest?
Correct Answer
$6400
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (SI) = 10%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 6
= $4000 ×10/100 × 6
= 4000 × 10 × 6/100
= 40000 × 6/100
= 240000/100
= $2400
Thus, Simple Interest = $2400
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 + $2400
= $6400
Thus, Amount to be paid = $6400 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) = 10%
And, Time (t) = 6 years
Thus, Amount (A)
= $4000 + ($4000 × 10% × 6)
= $4000 + ($4000 ×10/100 × 6)
= $4000 + (4000 × 10 × 6/100)
= $4000 + (40000 × 6/100)
= $4000 + (240000/100)
= $4000 + $2400 = $6400
Thus, Amount (A) to be paid = $6400 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $4000, the simple interest in 1 year
= 10/100 × 4000
= 10 × 4000/100
= 40000/100 = $400
Thus, simple interest for 1 year = $400
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $400 × 6 = $2400
Thus, Simple Interest (SI) = $2400
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $4000 + $2400
= $6400
Thus, Amount to be paid = $6400 Answer
Similar Questions
(1) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 5% simple interest?
(2) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $11316 to clear the loan, then find the time period of the loan.
(3) In how much time a principal of $3100 will amount to $3565 at a simple interest of 3% per annum?
(4) Calculate the amount due if William borrowed a sum of $3500 at 10% simple interest for 3 years.
(5) Kenneth had to pay $5300 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 8 years.
(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 10% simple interest for 8 years.
(8) How much loan did Jessica borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7187.5 to clear it?
(9) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8797.5 to clear it?
(10) What amount will be due after 2 years if Daniel borrowed a sum of $3550 at a 8% simple interest?