Question:
What amount does Patricia have to pay after 6 years if he takes a loan of $3150 at 10% simple interest?
Correct Answer
$5040
Solution And Explanation
Solution
Given,
Principal (P) = $3150
Rate of Simple Interest (SI) = 10%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 6
= $3150 ×10/100 × 6
= 3150 × 10 × 6/100
= 31500 × 6/100
= 189000/100
= $1890
Thus, Simple Interest = $1890
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 + $1890
= $5040
Thus, Amount to be paid = $5040 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) = 10%
And, Time (t) = 6 years
Thus, Amount (A)
= $3150 + ($3150 × 10% × 6)
= $3150 + ($3150 ×10/100 × 6)
= $3150 + (3150 × 10 × 6/100)
= $3150 + (31500 × 6/100)
= $3150 + (189000/100)
= $3150 + $1890 = $5040
Thus, Amount (A) to be paid = $5040 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3150, the simple interest in 1 year
= 10/100 × 3150
= 10 × 3150/100
= 31500/100 = $315
Thus, simple interest for 1 year = $315
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $315 × 6 = $1890
Thus, Simple Interest (SI) = $1890
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3150 + $1890
= $5040
Thus, Amount to be paid = $5040 Answer
Similar Questions
(1) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 8% simple interest?
(2) What amount does John have to pay after 5 years if he takes a loan of $3200 at 10% simple interest?
(3) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 8 years.
(4) James had to pay $3180 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(5) Find the amount to be paid if James borrowed a sum of $5000 at 7% simple interest for 7 years.
(6) Find the amount to be paid if Christopher borrowed a sum of $6000 at 3% simple interest for 7 years.
(7) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 7% simple interest?
(8) Anthony took a loan of $6600 at the rate of 6% simple interest per annum. If he paid an amount of $9768 to clear the loan, then find the time period of the loan.
(9) How much loan did Matthew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7440 to clear it?
(10) Calculate the amount due after 9 years if Christopher borrowed a sum of $6000 at a rate of 10% simple interest.