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) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 4 years.
(2) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 4% simple interest.
(3) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $10269 to clear the loan, then find the time period of the loan.
(4) How much loan did Karen borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6545 to clear it?
(5) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 4 years.
(6) William had to pay $3815 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) Betty took a loan of $6500 at the rate of 10% simple interest per annum. If he paid an amount of $12350 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Michael borrowed a sum of $3300 at 7% simple interest for 3 years.
(9) Calculate the amount due if Linda borrowed a sum of $3350 at 3% simple interest for 3 years.
(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 8% simple interest for 8 years.