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) Calculate the amount due if Karen borrowed a sum of $3950 at 2% simple interest for 4 years.
(2) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 9% simple interest.
(3) Jessica took a loan of $5500 at the rate of 10% simple interest per annum. If he paid an amount of $10450 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.
(5) Barbara had to pay $3976 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(6) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 8 years.
(7) Betty took a loan of $6500 at the rate of 8% simple interest per annum. If he paid an amount of $9620 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 7 years.
(9) Calculate the amount due if Elizabeth borrowed a sum of $3450 at 6% simple interest for 3 years.
(10) What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 2% simple interest?