Question:
Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 6% simple interest.
Correct Answer
$9163
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 6%
Time (t) = 9 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 9
= $5950 ×6/100 × 9
= 5950 × 6 × 9/100
= 35700 × 9/100
= 321300/100
= $3213
Thus, Simple Interest = $3213
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 + $3213
= $9163
Thus, Amount to be paid = $9163 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) = 6%
And, Time (t) = 9 years
Thus, Amount (A)
= $5950 + ($5950 × 6% × 9)
= $5950 + ($5950 ×6/100 × 9)
= $5950 + (5950 × 6 × 9/100)
= $5950 + (35700 × 9/100)
= $5950 + (321300/100)
= $5950 + $3213 = $9163
Thus, Amount (A) to be paid = $9163 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5950, the simple interest in 1 year
= 6/100 × 5950
= 6 × 5950/100
= 35700/100 = $357
Thus, simple interest for 1 year = $357
Therefore, simple interest for 9 years
= Simple interest for 1 year × 9
= $357 × 9 = $3213
Thus, Simple Interest (SI) = $3213
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $3213
= $9163
Thus, Amount to be paid = $9163 Answer
Similar Questions
(1) Michael took a loan of $4600 at the rate of 6% simple interest per annum. If he paid an amount of $7360 to clear the loan, then find the time period of the loan.
(2) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 7% simple interest.
(4) In how much time a principal of $3050 will amount to $3294 at a simple interest of 2% per annum?
(5) Calculate the amount due after 9 years if David borrowed a sum of $5400 at a rate of 2% simple interest.
(6) How much loan did Sharon borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8525 to clear it?
(7) Calculate the amount due after 10 years if Mary borrowed a sum of $5050 at a rate of 6% simple interest.
(8) Calculate the amount due after 10 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.
(9) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $12200 to clear the loan, then find the time period of the loan.
(10) How much loan did Linda borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $6152.5 to clear it?