Question:
What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 4% simple interest?
Correct Answer
$3906
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 4%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 6
= $3150 ×4/100 × 6
= 3150 × 4 × 6/100
= 12600 × 6/100
= 75600/100
= $756
Thus, Simple Interest = $756
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 + $756
= $3906
Thus, Amount to be paid = $3906 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) = 4%
And, Time (t) = 6 years
Thus, Amount (A)
= $3150 + ($3150 × 4% × 6)
= $3150 + ($3150 ×4/100 × 6)
= $3150 + (3150 × 4 × 6/100)
= $3150 + (12600 × 6/100)
= $3150 + (75600/100)
= $3150 + $756 = $3906
Thus, Amount (A) to be paid = $3906 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $3150, the simple interest in 1 year
= 4/100 × 3150
= 4 × 3150/100
= 12600/100 = $126
Thus, simple interest for 1 year = $126
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $126 × 6 = $756
Thus, Simple Interest (SI) = $756
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $756
= $3906
Thus, Amount to be paid = $3906 Answer
Similar Questions
(1) If Sarah paid $4620 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 2% simple interest for 4 years.
(3) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 9% simple interest.
(4) In how much time a principal of $3200 will amount to $3392 at a simple interest of 3% per annum?
(5) Find the amount to be paid if Christopher borrowed a sum of $6000 at 4% simple interest for 7 years.
(6) Sandra took a loan of $6900 at the rate of 9% simple interest per annum. If he paid an amount of $10626 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 8 years.
(8) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 2% simple interest.
(9) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(10) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.