Question:
What amount does Michael have to pay after 6 years if he takes a loan of $3300 at 7% simple interest?
Correct Answer
$4686
Solution And Explanation
Solution
Given,
Principal (P) = $3300
Rate of Simple Interest (SI) = 7%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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) = $3300 × 7% × 6
= $3300 ×7/100 × 6
= 3300 × 7 × 6/100
= 23100 × 6/100
= 138600/100
= $1386
Thus, Simple Interest = $1386
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 = $3300 + $1386
= $4686
Thus, Amount to be paid = $4686 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 = $3300
Rate of Simple Interest (SI) or (R) = 7%
And, Time (t) = 6 years
Thus, Amount (A)
= $3300 + ($3300 × 7% × 6)
= $3300 + ($3300 ×7/100 × 6)
= $3300 + (3300 × 7 × 6/100)
= $3300 + (23100 × 6/100)
= $3300 + (138600/100)
= $3300 + $1386 = $4686
Thus, Amount (A) to be paid = $4686 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $3300, the simple interest in 1 year
= 7/100 × 3300
= 7 × 3300/100
= 23100/100 = $231
Thus, simple interest for 1 year = $231
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $231 × 6 = $1386
Thus, Simple Interest (SI) = $1386
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3300 + $1386
= $4686
Thus, Amount to be paid = $4686 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 6% simple interest.
(2) Calculate the amount due if Sarah borrowed a sum of $3850 at 3% simple interest for 3 years.
(3) Calculate the amount due if Sarah borrowed a sum of $3850 at 6% simple interest for 3 years.
(4) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9984 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 4 years.
(6) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
(7) John took a loan of $4400 at the rate of 8% simple interest per annum. If he paid an amount of $7216 to clear the loan, then find the time period of the loan.
(8) If David paid $4080 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 9% simple interest for 8 years.
(10) Patricia took a loan of $4300 at the rate of 10% simple interest per annum. If he paid an amount of $8170 to clear the loan, then find the time period of the loan.