Question:
Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 8 years.
Correct Answer
$8330
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 5%
Time (t) = 8 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) = $5950 × 5% × 8
= $5950 ×5/100 × 8
= 5950 × 5 × 8/100
= 29750 × 8/100
= 238000/100
= $2380
Thus, Simple Interest = $2380
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 = $5950 + $2380
= $8330
Thus, Amount to be paid = $8330 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 = $5950
Rate of Simple Interest (SI) or (R) = 5%
And, Time (t) = 8 years
Thus, Amount (A)
= $5950 + ($5950 × 5% × 8)
= $5950 + ($5950 ×5/100 × 8)
= $5950 + (5950 × 5 × 8/100)
= $5950 + (29750 × 8/100)
= $5950 + (238000/100)
= $5950 + $2380 = $8330
Thus, Amount (A) to be paid = $8330 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 $5950, the simple interest in 1 year
= 5/100 × 5950
= 5 × 5950/100
= 29750/100 = $297.5
Thus, simple interest for 1 year = $297.5
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $297.5 × 8 = $2380
Thus, Simple Interest (SI) = $2380
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $2380
= $8330
Thus, Amount to be paid = $8330 Answer
Similar Questions
(1) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9828 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 3 years.
(3) How much loan did Kevin borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7810 to clear it?
(4) Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 4 years.
(5) Calculate the amount due if Robert borrowed a sum of $3100 at 4% simple interest for 4 years.
(6) Calculate the amount due if David borrowed a sum of $3400 at 10% simple interest for 3 years.
(7) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 2% simple interest.
(8) If Andrew paid $5760 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(9) Find the amount to be paid if Robert borrowed a sum of $5100 at 4% simple interest for 8 years.
(10) Lisa took a loan of $6100 at the rate of 7% simple interest per annum. If he paid an amount of $10370 to clear the loan, then find the time period of the loan.