Question:
Calculate the amount due if John borrowed a sum of $3200 at 8% simple interest for 3 years.
Correct Answer
$3968
Solution And Explanation
Solution
Given,
Principal (P) = $3200
Rate of Simple Interest (SI) = 8%
Time (t) = 3 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% × 3
= $3200 ×8/100 × 3
= 3200 × 8 × 3/100
= 25600 × 3/100
= 76800/100
= $768
Thus, Simple Interest = $768
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 + $768
= $3968
Thus, Amount to be paid = $3968 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) = 3 years
Thus, Amount (A)
= $3200 + ($3200 × 8% × 3)
= $3200 + ($3200 ×8/100 × 3)
= $3200 + (3200 × 8 × 3/100)
= $3200 + (25600 × 3/100)
= $3200 + (76800/100)
= $3200 + $768 = $3968
Thus, Amount (A) to be paid = $3968 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 3 years
= Simple interest for 1 year × 3
= $256 × 3 = $768
Thus, Simple Interest (SI) = $768
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3200 + $768
= $3968
Thus, Amount to be paid = $3968 Answer
Similar Questions
(1) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 7 years.
(2) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 7% simple interest.
(3) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.
(4) Sarah had to pay $4081 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.
(6) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 8% simple interest?
(7) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 8% simple interest.
(9) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9514 to clear the loan, then find the time period of the loan.
(10) In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?