Question:
Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 4% simple interest.
Correct Answer
$8092
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 4%
Time (t) = 9 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% × 9
= $5950 ×4/100 × 9
= 5950 × 4 × 9/100
= 23800 × 9/100
= 214200/100
= $2142
Thus, Simple Interest = $2142
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 + $2142
= $8092
Thus, Amount to be paid = $8092 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) = 9 years
Thus, Amount (A)
= $5950 + ($5950 × 4% × 9)
= $5950 + ($5950 ×4/100 × 9)
= $5950 + (5950 × 4 × 9/100)
= $5950 + (23800 × 9/100)
= $5950 + (214200/100)
= $5950 + $2142 = $8092
Thus, Amount (A) to be paid = $8092 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 9 years
= Simple interest for 1 year × 9
= $238 × 9 = $2142
Thus, Simple Interest (SI) = $2142
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $2142
= $8092
Thus, Amount to be paid = $8092 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 10% simple interest.
(2) Patricia took a loan of $4300 at the rate of 9% simple interest per annum. If he paid an amount of $6622 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 7 years.
(4) Calculate the amount due if David borrowed a sum of $3400 at 2% simple interest for 3 years.
(5) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 6% simple interest.
(6) Find the amount to be paid if John borrowed a sum of $5200 at 7% simple interest for 7 years.
(7) Lisa took a loan of $6100 at the rate of 6% simple interest per annum. If he paid an amount of $9028 to clear the loan, then find the time period of the loan.
(8) What amount does Mary have to pay after 5 years if he takes a loan of $3050 at 5% simple interest?
(9) 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.
(10) Calculate the amount due after 10 years if Barbara borrowed a sum of $5550 at a rate of 8% simple interest.