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) How much loan did Barbara borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $6105 to clear it?
(2) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 8 years.
(3) What amount does David have to pay after 5 years if he takes a loan of $3400 at 7% simple interest?
(4) Calculate the amount due if Jessica borrowed a sum of $3750 at 10% simple interest for 4 years.
(5) What amount does John have to pay after 5 years if he takes a loan of $3200 at 6% simple interest?
(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 7 years.
(7) Patricia took a loan of $4300 at the rate of 8% simple interest per annum. If he paid an amount of $6364 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due after 9 years if Michael borrowed a sum of $5300 at a rate of 4% simple interest.
(9) Find the amount to be paid if Charles borrowed a sum of $5900 at 2% simple interest for 7 years.
(10) Calculate the amount due after 10 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.