Question:
Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 9% simple interest.
Correct Answer
$9321.5
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 9%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 9% simple interest means, Rate of Simple Interest (SI) is 9% 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 × 9% × 9
= $5150 ×9/100 × 9
= 5150 × 9 × 9/100
= 46350 × 9/100
= 417150/100
= $4171.5
Thus, Simple Interest = $4171.5
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 + $4171.5
= $9321.5
Thus, Amount to be paid = $9321.5 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) = 9%
And, Time (t) = 9 years
Thus, Amount (A)
= $5150 + ($5150 × 9% × 9)
= $5150 + ($5150 ×9/100 × 9)
= $5150 + (5150 × 9 × 9/100)
= $5150 + (46350 × 9/100)
= $5150 + (417150/100)
= $5150 + $4171.5 = $9321.5
Thus, Amount (A) to be paid = $9321.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 9%
This, means, $9 per $100 per year
∵ For $100, the simple interest for 1 year = $9
∴ For $1, the simple interest for 1 year = 9/100
∴ For $5150, the simple interest in 1 year
= 9/100 × 5150
= 9 × 5150/100
= 46350/100 = $463.5
Thus, simple interest for 1 year = $463.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $463.5 × 9 = $4171.5
Thus, Simple Interest (SI) = $4171.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $4171.5
= $9321.5
Thus, Amount to be paid = $9321.5 Answer
Similar Questions
(1) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 2% simple interest for 7 years.
(2) Calculate the amount due if Mary borrowed a sum of $3050 at 4% simple interest for 3 years.
(3) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 10% simple interest?
(4) Find the amount to be paid if Elizabeth borrowed a sum of $5450 at 6% simple interest for 8 years.
(5) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 9% simple interest?
(6) Find the amount to be paid if Richard borrowed a sum of $5600 at 5% simple interest for 7 years.
(7) How much loan did Deborah borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $9312.5 to clear it?
(8) Richard took a loan of $5200 at the rate of 7% simple interest per annum. If he paid an amount of $7384 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 8 years.
(10) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $12400 to clear the loan, then find the time period of the loan.