Question:
Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 8% simple interest.
Correct Answer
$8858
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 8%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 9
= $5150 ×8/100 × 9
= 5150 × 8 × 9/100
= 41200 × 9/100
= 370800/100
= $3708
Thus, Simple Interest = $3708
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 + $3708
= $8858
Thus, Amount to be paid = $8858 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) = 8%
And, Time (t) = 9 years
Thus, Amount (A)
= $5150 + ($5150 × 8% × 9)
= $5150 + ($5150 ×8/100 × 9)
= $5150 + (5150 × 8 × 9/100)
= $5150 + (41200 × 9/100)
= $5150 + (370800/100)
= $5150 + $3708 = $8858
Thus, Amount (A) to be paid = $8858 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5150, the simple interest in 1 year
= 8/100 × 5150
= 8 × 5150/100
= 41200/100 = $412
Thus, simple interest for 1 year = $412
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $412 × 9 = $3708
Thus, Simple Interest (SI) = $3708
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $3708
= $8858
Thus, Amount to be paid = $8858 Answer
Similar Questions
(1) How much loan did Laura borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8635 to clear it?
(2) If Linda paid $3618 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(3) Richard took a loan of $5200 at the rate of 6% simple interest per annum. If he paid an amount of $7696 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 4% simple interest.
(5) In how much time a principal of $3050 will amount to $3507.5 at a simple interest of 3% per annum?
(6) If Jennifer borrowed $3250 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
(7) Barbara took a loan of $5100 at the rate of 9% simple interest per annum. If he paid an amount of $7854 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Linda borrowed a sum of $3350 at 7% simple interest for 3 years.
(9) What amount does David have to pay after 6 years if he takes a loan of $3400 at 9% simple interest?
(10) Find the amount to be paid if Christopher borrowed a sum of $6000 at 8% simple interest for 7 years.