Question:
What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 6% simple interest?
Correct Answer
$4284
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 6%
Time (t) = 6 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) = $3150 × 6% × 6
= $3150 ×6/100 × 6
= 3150 × 6 × 6/100
= 18900 × 6/100
= 113400/100
= $1134
Thus, Simple Interest = $1134
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 = $3150 + $1134
= $4284
Thus, Amount to be paid = $4284 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 = $3150
Rate of Simple Interest (SI) or (R) = 6%
And, Time (t) = 6 years
Thus, Amount (A)
= $3150 + ($3150 × 6% × 6)
= $3150 + ($3150 ×6/100 × 6)
= $3150 + (3150 × 6 × 6/100)
= $3150 + (18900 × 6/100)
= $3150 + (113400/100)
= $3150 + $1134 = $4284
Thus, Amount (A) to be paid = $4284 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 $3150, the simple interest in 1 year
= 6/100 × 3150
= 6 × 3150/100
= 18900/100 = $189
Thus, simple interest for 1 year = $189
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $189 × 6 = $1134
Thus, Simple Interest (SI) = $1134
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $1134
= $4284
Thus, Amount to be paid = $4284 Answer
Similar Questions
(1) Find the amount to be paid if Joseph borrowed a sum of $5700 at 4% simple interest for 8 years.
(2) Joseph had to pay $4255 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Mark took a loan of $6800 at the rate of 7% simple interest per annum. If he paid an amount of $11084 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 10% simple interest.
(5) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 8% simple interest.
(6) Find the amount to be paid if Patricia borrowed a sum of $5150 at 8% simple interest for 8 years.
(7) Michelle had to pay $5544 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(8) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11352 to clear the loan, then find the time period of the loan.
(9) What amount will be due after 2 years if John borrowed a sum of $3100 at a 7% simple interest?
(10) Karen had to pay $4542.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.