Question:
Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 8 years.
Correct Answer
$7854
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 4%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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 × 4% × 8
= $5950 ×4/100 × 8
= 5950 × 4 × 8/100
= 23800 × 8/100
= 190400/100
= $1904
Thus, Simple Interest = $1904
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 + $1904
= $7854
Thus, Amount to be paid = $7854 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) = 4%
And, Time (t) = 8 years
Thus, Amount (A)
= $5950 + ($5950 × 4% × 8)
= $5950 + ($5950 ×4/100 × 8)
= $5950 + (5950 × 4 × 8/100)
= $5950 + (23800 × 8/100)
= $5950 + (190400/100)
= $5950 + $1904 = $7854
Thus, Amount (A) to be paid = $7854 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5950, the simple interest in 1 year
= 4/100 × 5950
= 4 × 5950/100
= 23800/100 = $238
Thus, simple interest for 1 year = $238
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $238 × 8 = $1904
Thus, Simple Interest (SI) = $1904
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $1904
= $7854
Thus, Amount to be paid = $7854 Answer
Similar Questions
(1) Christopher took a loan of $6000 at the rate of 10% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 10% simple interest.
(3) Calculate the amount due if Michael borrowed a sum of $3300 at 6% simple interest for 3 years.
(4) If Michelle paid $5346 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(5) If Robert borrowed $3100 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(6) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.
(7) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 8% simple interest?
(8) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 10% simple interest.
(9) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 4 years.
(10) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.