Question:
Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 3 years.
Correct Answer
$3776
Solution And Explanation
Solution
Given,
Principal (P) = $3200
Rate of Simple Interest (SI) = 6%
Time (t) = 3 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 3
= $3200 ×6/100 × 3
= 3200 × 6 × 3/100
= 19200 × 3/100
= 57600/100
= $576
Thus, Simple Interest = $576
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 + $576
= $3776
Thus, Amount to be paid = $3776 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) = 6%
And, Time (t) = 3 years
Thus, Amount (A)
= $3200 + ($3200 × 6% × 3)
= $3200 + ($3200 ×6/100 × 3)
= $3200 + (3200 × 6 × 3/100)
= $3200 + (19200 × 3/100)
= $3200 + (57600/100)
= $3200 + $576 = $3776
Thus, Amount (A) to be paid = $3776 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $3200, the simple interest in 1 year
= 6/100 × 3200
= 6 × 3200/100
= 19200/100 = $192
Thus, simple interest for 1 year = $192
Therefore, simple interest for 3 years
= Simple interest for 1 year × 3
= $192 × 3 = $576
Thus, Simple Interest (SI) = $576
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3200 + $576
= $3776
Thus, Amount to be paid = $3776 Answer
Similar Questions
(1) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.
(2) David took a loan of $4800 at the rate of 8% simple interest per annum. If he paid an amount of $7104 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 8 years.
(4) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.
(5) John took a loan of $4400 at the rate of 7% simple interest per annum. If he paid an amount of $6864 to clear the loan, then find the time period of the loan.
(6) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 7 years.
(7) Donald took a loan of $7000 at the rate of 8% simple interest per annum. If he paid an amount of $10920 to clear the loan, then find the time period of the loan.
(8) Sandra took a loan of $6900 at the rate of 6% simple interest per annum. If he paid an amount of $11040 to clear the loan, then find the time period of the loan.
(9) Joseph took a loan of $5400 at the rate of 8% simple interest per annum. If he paid an amount of $8424 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due after 10 years if Christopher borrowed a sum of $6000 at a rate of 9% simple interest.