Question:
What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 7% simple interest?
Correct Answer
$5680
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (SI) = 7%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 6
= $4000 ×7/100 × 6
= 4000 × 7 × 6/100
= 28000 × 6/100
= 168000/100
= $1680
Thus, Simple Interest = $1680
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 + $1680
= $5680
Thus, Amount to be paid = $5680 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) = 7%
And, Time (t) = 6 years
Thus, Amount (A)
= $4000 + ($4000 × 7% × 6)
= $4000 + ($4000 ×7/100 × 6)
= $4000 + (4000 × 7 × 6/100)
= $4000 + (28000 × 6/100)
= $4000 + (168000/100)
= $4000 + $1680 = $5680
Thus, Amount (A) to be paid = $5680 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $4000, the simple interest in 1 year
= 7/100 × 4000
= 7 × 4000/100
= 28000/100 = $280
Thus, simple interest for 1 year = $280
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $280 × 6 = $1680
Thus, Simple Interest (SI) = $1680
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $4000 + $1680
= $5680
Thus, Amount to be paid = $5680 Answer
Similar Questions
(1) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7003 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.
(3) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 7 years.
(4) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 4% simple interest.
(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 5% simple interest for 3 years.
(6) Calculate the amount due if Karen borrowed a sum of $3950 at 10% simple interest for 4 years.
(7) What amount will be due after 2 years if Kenneth borrowed a sum of $4000 at a 6% simple interest?
(8) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 3% simple interest.
(9) Calculate the amount due if Charles borrowed a sum of $3900 at 4% simple interest for 4 years.
(10) Robert had to pay $3379 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.