Question:
Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 8 years.
Correct Answer
$8806
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 6%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 8
= $5950 ×6/100 × 8
= 5950 × 6 × 8/100
= 35700 × 8/100
= 285600/100
= $2856
Thus, Simple Interest = $2856
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 + $2856
= $8806
Thus, Amount to be paid = $8806 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) = 6%
And, Time (t) = 8 years
Thus, Amount (A)
= $5950 + ($5950 × 6% × 8)
= $5950 + ($5950 ×6/100 × 8)
= $5950 + (5950 × 6 × 8/100)
= $5950 + (35700 × 8/100)
= $5950 + (285600/100)
= $5950 + $2856 = $8806
Thus, Amount (A) to be paid = $8806 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5950, the simple interest in 1 year
= 6/100 × 5950
= 6 × 5950/100
= 35700/100 = $357
Thus, simple interest for 1 year = $357
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $357 × 8 = $2856
Thus, Simple Interest (SI) = $2856
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $2856
= $8806
Thus, Amount to be paid = $8806 Answer
Similar Questions
(1) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $10440 to clear the loan, then find the time period of the loan.
(2) If Matthew paid $4704 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(3) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $7396 to clear the loan, then find the time period of the loan.
(4) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 5% simple interest for 7 years.
(5) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 2% simple interest.
(6) Thomas took a loan of $5600 at the rate of 10% simple interest per annum. If he paid an amount of $9520 to clear the loan, then find the time period of the loan.
(7) Charles took a loan of $5800 at the rate of 10% simple interest per annum. If he paid an amount of $11600 to clear the loan, then find the time period of the loan.
(8) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.
(9) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 8% simple interest?
(10) Find the amount to be paid if Jessica borrowed a sum of $5750 at 9% simple interest for 7 years.