Question:
Calculate the amount due if Christopher borrowed a sum of $4000 at 8% simple interest for 4 years.
Correct Answer
$5280
Solution And Explanation
Solution
Given,
Principal (P) = $4000
Rate of Simple Interest (SI) = 8%
Time (t) = 4 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% × 4
= $4000 ×8/100 × 4
= 4000 × 8 × 4/100
= 32000 × 4/100
= 128000/100
= $1280
Thus, Simple Interest = $1280
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 + $1280
= $5280
Thus, Amount to be paid = $5280 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) = 4 years
Thus, Amount (A)
= $4000 + ($4000 × 8% × 4)
= $4000 + ($4000 ×8/100 × 4)
= $4000 + (4000 × 8 × 4/100)
= $4000 + (32000 × 4/100)
= $4000 + (128000/100)
= $4000 + $1280 = $5280
Thus, Amount (A) to be paid = $5280 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 4 years
= Simple interest for 1 year × 4
= $320 × 4 = $1280
Thus, Simple Interest (SI) = $1280
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $4000 + $1280
= $5280
Thus, Amount to be paid = $5280 Answer
Similar Questions
(1) How much loan did Donna borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8220 to clear it?
(2) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7242 to clear the loan, then find the time period of the loan.
(3) Karen took a loan of $5900 at the rate of 8% simple interest per annum. If he paid an amount of $10620 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 7% simple interest.
(5) Find the amount to be paid if John borrowed a sum of $5200 at 10% simple interest for 7 years.
(6) Calculate the amount due after 9 years if Susan borrowed a sum of $5650 at a rate of 2% simple interest.
(7) Find the amount to be paid if Michael borrowed a sum of $5300 at 8% simple interest for 8 years.
(8) Richard took a loan of $5200 at the rate of 10% simple interest per annum. If he paid an amount of $10400 to clear the loan, then find the time period of the loan.
(9) What amount does Mary have to pay after 6 years if he takes a loan of $3050 at 7% simple interest?
(10) What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 6% simple interest?