Question:
Find the amount to be paid if Karen borrowed a sum of $5950 at 4% simple interest for 8 years.
Correct Answer
$7854
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 4%
Time (t) = 8 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% × 8
= $5950 ×4/100 × 8
= 5950 × 4 × 8/100
= 23800 × 8/100
= 190400/100
= $1904
Thus, Simple Interest = $1904
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 + $1904
= $7854
Thus, Amount to be paid = $7854 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) = 8 years
Thus, Amount (A)
= $5950 + ($5950 × 4% × 8)
= $5950 + ($5950 ×4/100 × 8)
= $5950 + (5950 × 4 × 8/100)
= $5950 + (23800 × 8/100)
= $5950 + (190400/100)
= $5950 + $1904 = $7854
Thus, Amount (A) to be paid = $7854 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 8 years
= Simple interest for 1 year × 8
= $238 × 8 = $1904
Thus, Simple Interest (SI) = $1904
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $1904
= $7854
Thus, Amount to be paid = $7854 Answer
Similar Questions
(1) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.
(2) Find the amount to be paid if Karen borrowed a sum of $5950 at 3% simple interest for 8 years.
(3) How much loan did Robert borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6375 to clear it?
(4) How much loan did Paul borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8375 to clear it?
(5) How much loan did Stephanie borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8305 to clear it?
(6) Linda took a loan of $4700 at the rate of 7% simple interest per annum. If he paid an amount of $7990 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if Linda borrowed a sum of $5350 at 5% simple interest for 7 years.
(8) In how much time a principal of $3050 will amount to $3233 at a simple interest of 3% per annum?
(9) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 2% simple interest?
(10) Nancy took a loan of $6300 at the rate of 9% simple interest per annum. If he paid an amount of $11970 to clear the loan, then find the time period of the loan.