Question:
Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 8 years.
Correct Answer
$9758
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 8%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 8
= $5950 ×8/100 × 8
= 5950 × 8 × 8/100
= 47600 × 8/100
= 380800/100
= $3808
Thus, Simple Interest = $3808
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 + $3808
= $9758
Thus, Amount to be paid = $9758 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) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $5950 + ($5950 × 8% × 8)
= $5950 + ($5950 ×8/100 × 8)
= $5950 + (5950 × 8 × 8/100)
= $5950 + (47600 × 8/100)
= $5950 + (380800/100)
= $5950 + $3808 = $9758
Thus, Amount (A) to be paid = $9758 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5950, the simple interest in 1 year
= 8/100 × 5950
= 8 × 5950/100
= 47600/100 = $476
Thus, simple interest for 1 year = $476
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $476 × 8 = $3808
Thus, Simple Interest (SI) = $3808
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $3808
= $9758
Thus, Amount to be paid = $9758 Answer
Similar Questions
(1) Find the amount to be paid if Richard borrowed a sum of $5600 at 3% simple interest for 7 years.
(2) Patricia had to pay $3433.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $5440 to clear the loan, then find the time period of the loan.
(4) Thomas had to pay $4256 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 8 years.
(6) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 3% simple interest?
(7) Charles took a loan of $5800 at the rate of 6% simple interest per annum. If he paid an amount of $7888 to clear the loan, then find the time period of the loan.
(8) Matthew took a loan of $6400 at the rate of 6% simple interest per annum. If he paid an amount of $10240 to clear the loan, then find the time period of the loan.
(9) Michael took a loan of $4600 at the rate of 8% simple interest per annum. If he paid an amount of $8280 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Robert borrowed a sum of $3100 at 5% simple interest for 3 years.