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) How much loan did Rebecca borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8797.5 to clear it?
(2) Richard took a loan of $5200 at the rate of 8% simple interest per annum. If he paid an amount of $8528 to clear the loan, then find the time period of the loan.
(3) Anthony had to pay $4945 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(4) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(5) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 7% simple interest.
(6) Robert took a loan of $4200 at the rate of 7% simple interest per annum. If he paid an amount of $7140 to clear the loan, then find the time period of the loan.
(7) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7315 to clear it?
(8) Calculate the amount due if Karen borrowed a sum of $3950 at 7% simple interest for 3 years.
(9) Calculate the amount due after 9 years if Richard borrowed a sum of $5600 at a rate of 10% simple interest.
(10) What amount does William have to pay after 5 years if he takes a loan of $3500 at 10% simple interest?