Question:
Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.
Correct Answer
$8627.5
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 5%
Time (t) = 9 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% × 9
= $5950 ×5/100 × 9
= 5950 × 5 × 9/100
= 29750 × 9/100
= 267750/100
= $2677.5
Thus, Simple Interest = $2677.5
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 + $2677.5
= $8627.5
Thus, Amount to be paid = $8627.5 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) = 9 years
Thus, Amount (A)
= $5950 + ($5950 × 5% × 9)
= $5950 + ($5950 ×5/100 × 9)
= $5950 + (5950 × 5 × 9/100)
= $5950 + (29750 × 9/100)
= $5950 + (267750/100)
= $5950 + $2677.5 = $8627.5
Thus, Amount (A) to be paid = $8627.5 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 9 years
= Simple interest for 1 year × 9
= $297.5 × 9 = $2677.5
Thus, Simple Interest (SI) = $2677.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $2677.5
= $8627.5
Thus, Amount to be paid = $8627.5 Answer
Similar Questions
(1) What amount will be due after 2 years if David borrowed a sum of $3200 at a 5% simple interest?
(2) Mark had to pay $5060 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(3) Find the amount to be paid if John borrowed a sum of $5200 at 5% simple interest for 7 years.
(4) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 6% simple interest?
(5) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 7 years.
(6) If David borrowed $3400 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(7) Michael took a loan of $4600 at the rate of 10% simple interest per annum. If he paid an amount of $8740 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if Thomas borrowed a sum of $5800 at 9% simple interest for 7 years.
(9) Calculate the amount due if Jennifer borrowed a sum of $3250 at 10% simple interest for 4 years.
(10) Daniel took a loan of $6200 at the rate of 8% simple interest per annum. If he paid an amount of $11160 to clear the loan, then find the time period of the loan.