Question:
Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 4 years.
Correct Answer
$4224
Solution And Explanation
Solution
Given,
Principal (P) = $3200
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) = $3200 × 8% × 4
= $3200 ×8/100 × 4
= 3200 × 8 × 4/100
= 25600 × 4/100
= 102400/100
= $1024
Thus, Simple Interest = $1024
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 = $3200 + $1024
= $4224
Thus, Amount to be paid = $4224 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 = $3200
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 4 years
Thus, Amount (A)
= $3200 + ($3200 × 8% × 4)
= $3200 + ($3200 ×8/100 × 4)
= $3200 + (3200 × 8 × 4/100)
= $3200 + (25600 × 4/100)
= $3200 + (102400/100)
= $3200 + $1024 = $4224
Thus, Amount (A) to be paid = $4224 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 $3200, the simple interest in 1 year
= 8/100 × 3200
= 8 × 3200/100
= 25600/100 = $256
Thus, simple interest for 1 year = $256
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $256 × 4 = $1024
Thus, Simple Interest (SI) = $1024
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3200 + $1024
= $4224
Thus, Amount to be paid = $4224 Answer
Similar Questions
(1) What amount does William have to pay after 5 years if he takes a loan of $3500 at 3% simple interest?
(2) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $11700 to clear the loan, then find the time period of the loan.
(3) In how much time a principal of $3000 will amount to $3360 at a simple interest of 4% per annum?
(4) Patricia took a loan of $4300 at the rate of 6% simple interest per annum. If he paid an amount of $5848 to clear the loan, then find the time period of the loan.
(5) Steven had to pay $5152 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) Find the amount to be paid if William borrowed a sum of $5500 at 9% simple interest for 8 years.
(7) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 10% simple interest?
(8) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 10% simple interest?
(9) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $10608 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 7% simple interest.