Question:
Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 6% simple interest.
Correct Answer
$7931
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 6%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 9
= $5150 ×6/100 × 9
= 5150 × 6 × 9/100
= 30900 × 9/100
= 278100/100
= $2781
Thus, Simple Interest = $2781
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 + $2781
= $7931
Thus, Amount to be paid = $7931 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) = 6%
And, Time (t) = 9 years
Thus, Amount (A)
= $5150 + ($5150 × 6% × 9)
= $5150 + ($5150 ×6/100 × 9)
= $5150 + (5150 × 6 × 9/100)
= $5150 + (30900 × 9/100)
= $5150 + (278100/100)
= $5150 + $2781 = $7931
Thus, Amount (A) to be paid = $7931 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5150, the simple interest in 1 year
= 6/100 × 5150
= 6 × 5150/100
= 30900/100 = $309
Thus, simple interest for 1 year = $309
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $309 × 9 = $2781
Thus, Simple Interest (SI) = $2781
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $2781
= $7931
Thus, Amount to be paid = $7931 Answer
Similar Questions
(1) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $11590 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 7 years.
(3) In how much time a principal of $3050 will amount to $3324.5 at a simple interest of 3% per annum?
(4) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 5% simple interest?
(5) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 7 years.
(6) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 2% simple interest.
(7) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 9% simple interest?
(8) In how much time a principal of $3200 will amount to $3712 at a simple interest of 4% per annum?
(9) What amount does Susan have to pay after 5 years if he takes a loan of $3650 at 9% simple interest?
(10) Daniel took a loan of $6200 at the rate of 9% simple interest per annum. If he paid an amount of $10664 to clear the loan, then find the time period of the loan.