Question:
Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 5% simple interest.
Correct Answer
$7467.5
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 5%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 9
= $5150 ×5/100 × 9
= 5150 × 5 × 9/100
= 25750 × 9/100
= 231750/100
= $2317.5
Thus, Simple Interest = $2317.5
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 + $2317.5
= $7467.5
Thus, Amount to be paid = $7467.5 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) = 5%
And, Time (t) = 9 years
Thus, Amount (A)
= $5150 + ($5150 × 5% × 9)
= $5150 + ($5150 ×5/100 × 9)
= $5150 + (5150 × 5 × 9/100)
= $5150 + (25750 × 9/100)
= $5150 + (231750/100)
= $5150 + $2317.5 = $7467.5
Thus, Amount (A) to be paid = $7467.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5150, the simple interest in 1 year
= 5/100 × 5150
= 5 × 5150/100
= 25750/100 = $257.5
Thus, simple interest for 1 year = $257.5
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $257.5 × 9 = $2317.5
Thus, Simple Interest (SI) = $2317.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $2317.5
= $7467.5
Thus, Amount to be paid = $7467.5 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 4% simple interest.
(2) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $9128 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 3 years.
(4) Michael took a loan of $4600 at the rate of 9% simple interest per annum. If he paid an amount of $7498 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 8% simple interest.
(6) In how much time a principal of $3200 will amount to $3712 at a simple interest of 4% per annum?
(7) If Joshua paid $5488 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(8) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 4% simple interest?
(9) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $8662 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if James borrowed a sum of $3000 at 4% simple interest for 4 years.