Question:
Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 7 years.
Correct Answer
$8449
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 6%
Time (t) = 7 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% × 7
= $5950 ×6/100 × 7
= 5950 × 6 × 7/100
= 35700 × 7/100
= 249900/100
= $2499
Thus, Simple Interest = $2499
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 + $2499
= $8449
Thus, Amount to be paid = $8449 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) = 7 years
Thus, Amount (A)
= $5950 + ($5950 × 6% × 7)
= $5950 + ($5950 ×6/100 × 7)
= $5950 + (5950 × 6 × 7/100)
= $5950 + (35700 × 7/100)
= $5950 + (249900/100)
= $5950 + $2499 = $8449
Thus, Amount (A) to be paid = $8449 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 7 years
= Simple interest for 1 year × 7
= $357 × 7 = $2499
Thus, Simple Interest (SI) = $2499
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $2499
= $8449
Thus, Amount to be paid = $8449 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 $12060 to clear the loan, then find the time period of the loan.
(2) In how much time a principal of $3100 will amount to $3286 at a simple interest of 2% per annum?
(3) Donna had to pay $5286.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) Calculate the amount due after 9 years if Robert borrowed a sum of $5100 at a rate of 9% simple interest.
(5) How much loan did Betty borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6875 to clear it?
(6) Christopher had to pay $4480 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(7) Find the amount to be paid if Patricia borrowed a sum of $5150 at 5% simple interest for 7 years.
(8) What amount will be due after 2 years if Richard borrowed a sum of $3300 at a 10% simple interest?
(9) How much loan did Amanda borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $7865 to clear it?
(10) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8337.5 to clear it?