Question:
Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 4% simple interest.
Correct Answer
$7004
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 4%
Time (t) = 9 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% × 9
= $5150 ×4/100 × 9
= 5150 × 4 × 9/100
= 20600 × 9/100
= 185400/100
= $1854
Thus, Simple Interest = $1854
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 + $1854
= $7004
Thus, Amount to be paid = $7004 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) = 9 years
Thus, Amount (A)
= $5150 + ($5150 × 4% × 9)
= $5150 + ($5150 ×4/100 × 9)
= $5150 + (5150 × 4 × 9/100)
= $5150 + (20600 × 9/100)
= $5150 + (185400/100)
= $5150 + $1854 = $7004
Thus, Amount (A) to be paid = $7004 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 9 years
= Simple interest for 1 year × 9
= $206 × 9 = $1854
Thus, Simple Interest (SI) = $1854
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $1854
= $7004
Thus, Amount to be paid = $7004 Answer
Similar Questions
(1) Find the amount to be paid if David borrowed a sum of $5400 at 3% simple interest for 8 years.
(2) Margaret had to pay $4741.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) If Thomas borrowed $3800 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(4) Joshua had to pay $5341 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $6705 to clear the loan, then find the time period of the loan.
(6) Calculate the amount due if Susan borrowed a sum of $3650 at 7% simple interest for 3 years.
(7) Find the amount to be paid if Sarah borrowed a sum of $5850 at 4% simple interest for 8 years.
(8) Robert had to pay $3379 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) If Ashley paid $4914 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(10) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.