Question:
Find the amount to be paid if Patricia borrowed a sum of $5150 at 2% simple interest for 8 years.
Correct Answer
$5974
Solution And Explanation
Solution
Given,
Principal (P) = $5150
Rate of Simple Interest (SI) = 2%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 8
= $5150 ×2/100 × 8
= 5150 × 2 × 8/100
= 10300 × 8/100
= 82400/100
= $824
Thus, Simple Interest = $824
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 + $824
= $5974
Thus, Amount to be paid = $5974 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) = 2%
And, Time (t) = 8 years
Thus, Amount (A)
= $5150 + ($5150 × 2% × 8)
= $5150 + ($5150 ×2/100 × 8)
= $5150 + (5150 × 2 × 8/100)
= $5150 + (10300 × 8/100)
= $5150 + (82400/100)
= $5150 + $824 = $5974
Thus, Amount (A) to be paid = $5974 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $5150, the simple interest in 1 year
= 2/100 × 5150
= 2 × 5150/100
= 10300/100 = $103
Thus, simple interest for 1 year = $103
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $103 × 8 = $824
Thus, Simple Interest (SI) = $824
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5150 + $824
= $5974
Thus, Amount to be paid = $5974 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Patricia borrowed a sum of $5150 at a rate of 2% simple interest.
(2) Find the amount to be paid if Christopher borrowed a sum of $6000 at 10% simple interest for 7 years.
(3) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 5% simple interest.
(4) Daniel took a loan of $6200 at the rate of 6% simple interest per annum. If he paid an amount of $8432 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if James borrowed a sum of $5000 at 6% simple interest for 7 years.
(6) Calculate the amount due if William borrowed a sum of $3500 at 8% simple interest for 4 years.
(7) Thomas took a loan of $5600 at the rate of 7% simple interest per annum. If he paid an amount of $8344 to clear the loan, then find the time period of the loan.
(8) If Paul paid $5452 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(9) If Betty paid $4930 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 3 years.