Question:
What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 8% simple interest?
Correct Answer
$5920
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (SI) = 8%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 6
= $4000 ×8/100 × 6
= 4000 × 8 × 6/100
= 32000 × 6/100
= 192000/100
= $1920
Thus, Simple Interest = $1920
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 + $1920
= $5920
Thus, Amount to be paid = $5920 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) = 8%
And, Time (t) = 6 years
Thus, Amount (A)
= $4000 + ($4000 × 8% × 6)
= $4000 + ($4000 ×8/100 × 6)
= $4000 + (4000 × 8 × 6/100)
= $4000 + (32000 × 6/100)
= $4000 + (192000/100)
= $4000 + $1920 = $5920
Thus, Amount (A) to be paid = $5920 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $4000, the simple interest in 1 year
= 8/100 × 4000
= 8 × 4000/100
= 32000/100 = $320
Thus, simple interest for 1 year = $320
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $320 × 6 = $1920
Thus, Simple Interest (SI) = $1920
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $4000 + $1920
= $5920
Thus, Amount to be paid = $5920 Answer
Similar Questions
(1) Find the amount to be paid if Sarah borrowed a sum of $5850 at 2% simple interest for 8 years.
(2) Calculate the amount due if James borrowed a sum of $3000 at 5% simple interest for 3 years.
(3) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.
(4) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9943 to clear the loan, then find the time period of the loan.
(5) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11600 to clear the loan, then find the time period of the loan.
(6) How much loan did Jessica borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6900 to clear it?
(7) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $10860 to clear the loan, then find the time period of the loan.
(8) If Michael paid $3564 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(9) How much loan did Amanda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8937.5 to clear it?
(10) John took a loan of $4400 at the rate of 6% simple interest per annum. If he paid an amount of $5984 to clear the loan, then find the time period of the loan.