Question:
Calculate the amount due after 10 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.
Correct Answer
$7210
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 4%
Time (t) = 10 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) = $5150 × 4% × 10
= $5150 ×4/100 × 10
= 5150 × 4 × 10/100
= 20600 × 10/100
= 206000/100
= $2060
Thus, Simple Interest = $2060
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 = $5150 + $2060
= $7210
Thus, Amount to be paid = $7210 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 = $5150
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 10 years
Thus, Amount (A)
= $5150 + ($5150 × 4% × 10)
= $5150 + ($5150 ×4/100 × 10)
= $5150 + (5150 × 4 × 10/100)
= $5150 + (20600 × 10/100)
= $5150 + (206000/100)
= $5150 + $2060 = $7210
Thus, Amount (A) to be paid = $7210 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 $5150, the simple interest in 1 year
= 4/100 × 5150
= 4 × 5150/100
= 20600/100 = $206
Thus, simple interest for 1 year = $206
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $206 × 10 = $2060
Thus, Simple Interest (SI) = $2060
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $2060
= $7210
Thus, Amount to be paid = $7210 Answer
Similar Questions
(1) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
(2) What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 2% simple interest?
(3) Find the amount to be paid if John borrowed a sum of $5200 at 6% simple interest for 8 years.
(4) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 2% simple interest?
(5) Find the amount to be paid if Patricia borrowed a sum of $5150 at 9% simple interest for 8 years.
(6) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 10% simple interest?
(7) Donald took a loan of $7000 at the rate of 7% simple interest per annum. If he paid an amount of $9940 to clear the loan, then find the time period of the loan.
(8) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 8% simple interest?
(9) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $9231 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 8 years.