Question:
Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
Correct Answer
$10234
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 8%
Time (t) = 9 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% × 9
= $5950 ×8/100 × 9
= 5950 × 8 × 9/100
= 47600 × 9/100
= 428400/100
= $4284
Thus, Simple Interest = $4284
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 + $4284
= $10234
Thus, Amount to be paid = $10234 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) = 9 years
Thus, Amount (A)
= $5950 + ($5950 × 8% × 9)
= $5950 + ($5950 ×8/100 × 9)
= $5950 + (5950 × 8 × 9/100)
= $5950 + (47600 × 9/100)
= $5950 + (428400/100)
= $5950 + $4284 = $10234
Thus, Amount (A) to be paid = $10234 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 9 years
= Simple interest for 1 year × 9
= $476 × 9 = $4284
Thus, Simple Interest (SI) = $4284
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $4284
= $10234
Thus, Amount to be paid = $10234 Answer
Similar Questions
(1) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $9916 to clear the loan, then find the time period of the loan.
(2) Jennifer took a loan of $4500 at the rate of 10% simple interest per annum. If he paid an amount of $8100 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due if Robert borrowed a sum of $3100 at 7% simple interest for 3 years.
(4) In how much time a principal of $3000 will amount to $3240 at a simple interest of 4% per annum?
(5) Find the amount to be paid if Robert borrowed a sum of $5100 at 6% simple interest for 7 years.
(6) Calculate the amount due if David borrowed a sum of $3400 at 6% simple interest for 4 years.
(7) What amount does Charles have to pay after 5 years if he takes a loan of $3900 at 4% simple interest?
(8) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 4 years.
(9) What amount does Thomas have to pay after 5 years if he takes a loan of $3800 at 9% simple interest?
(10) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 7 years.