Question:
Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 4 years.
Correct Answer
$3906
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 6%
Time (t) = 4 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% × 4
= $3150 ×6/100 × 4
= 3150 × 6 × 4/100
= 18900 × 4/100
= 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) = 6%
And, Time (t) = 4 years
Thus, Amount (A)
= $3150 + ($3150 × 6% × 4)
= $3150 + ($3150 ×6/100 × 4)
= $3150 + (3150 × 6 × 4/100)
= $3150 + (18900 × 4/100)
= $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 = 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 4 years
= Simple interest for 1 year × 4
= $189 × 4 = $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 Richard paid $3888 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(2) How much loan did Elizabeth borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6540 to clear it?
(3) Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 8 years.
(4) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 3 years.
(5) Find the amount to be paid if Susan borrowed a sum of $5650 at 6% simple interest for 7 years.
(6) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 9% simple interest?
(7) Donald took a loan of $7000 at the rate of 9% simple interest per annum. If he paid an amount of $11410 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 7 years.
(9) How much loan did Paul borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7370 to clear it?
(10) Elizabeth took a loan of $4900 at the rate of 7% simple interest per annum. If he paid an amount of $7644 to clear the loan, then find the time period of the loan.