Question:
What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 10% simple interest?
Correct Answer
$6000
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (SI) = 10%
Time (t) = 5 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% × 5
= $4000 ×10/100 × 5
= 4000 × 10 × 5/100
= 40000 × 5/100
= 200000/100
= $2000
Thus, Simple Interest = $2000
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 + $2000
= $6000
Thus, Amount to be paid = $6000 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) = 5 years
Thus, Amount (A)
= $4000 + ($4000 × 10% × 5)
= $4000 + ($4000 ×10/100 × 5)
= $4000 + (4000 × 10 × 5/100)
= $4000 + (40000 × 5/100)
= $4000 + (200000/100)
= $4000 + $2000 = $6000
Thus, Amount (A) to be paid = $6000 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 5 years
= Simple interest for 1 year × 5
= $400 × 5 = $2000
Thus, Simple Interest (SI) = $2000
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $4000 + $2000
= $6000
Thus, Amount to be paid = $6000 Answer
Similar Questions
(1) Find the amount to be paid if Jessica borrowed a sum of $5750 at 8% simple interest for 8 years.
(2) In how much time a principal of $3200 will amount to $3392 at a simple interest of 3% per annum?
(3) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 3 years.
(4) Calculate the amount due if Robert borrowed a sum of $3100 at 10% simple interest for 3 years.
(5) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 7% simple interest?
(6) Sarah had to pay $4427.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(7) John took a loan of $4400 at the rate of 10% simple interest per annum. If he paid an amount of $7920 to clear the loan, then find the time period of the loan.
(8) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9372 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 7 years.
(10) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 8 years.