Question:
Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 3% simple interest.
Correct Answer
$6540.5
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 3%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 9
= $5150 ×3/100 × 9
= 5150 × 3 × 9/100
= 15450 × 9/100
= 139050/100
= $1390.5
Thus, Simple Interest = $1390.5
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 + $1390.5
= $6540.5
Thus, Amount to be paid = $6540.5 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) = 3%
And, Time (t) = 9 years
Thus, Amount (A)
= $5150 + ($5150 × 3% × 9)
= $5150 + ($5150 ×3/100 × 9)
= $5150 + (5150 × 3 × 9/100)
= $5150 + (15450 × 9/100)
= $5150 + (139050/100)
= $5150 + $1390.5 = $6540.5
Thus, Amount (A) to be paid = $6540.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $5150, the simple interest in 1 year
= 3/100 × 5150
= 3 × 5150/100
= 15450/100 = $154.5
Thus, simple interest for 1 year = $154.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $154.5 × 9 = $1390.5
Thus, Simple Interest (SI) = $1390.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $1390.5
= $6540.5
Thus, Amount to be paid = $6540.5 Answer
Similar Questions
(1) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 8% simple interest for 8 years.
(2) In how much time a principal of $3000 will amount to $3300 at a simple interest of 2% per annum?
(3) Find the amount to be paid if Karen borrowed a sum of $5950 at 2% simple interest for 7 years.
(4) Mary took a loan of $4100 at the rate of 7% simple interest per annum. If he paid an amount of $6396 to clear the loan, then find the time period of the loan.
(5) What amount does Elizabeth have to pay after 5 years if he takes a loan of $3450 at 5% simple interest?
(6) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(7) How much loan did Anthony borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6930 to clear it?
(8) Anthony took a loan of $6600 at the rate of 7% simple interest per annum. If he paid an amount of $9834 to clear the loan, then find the time period of the loan.
(9) How much loan did Emily borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8100 to clear it?
(10) What amount will be due after 2 years if Thomas borrowed a sum of $3400 at a 10% simple interest?