Question:
Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 8 years.
Correct Answer
$8806
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 6%
Time (t) = 8 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% × 8
= $5950 ×6/100 × 8
= 5950 × 6 × 8/100
= 35700 × 8/100
= 285600/100
= $2856
Thus, Simple Interest = $2856
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 + $2856
= $8806
Thus, Amount to be paid = $8806 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) = 8 years
Thus, Amount (A)
= $5950 + ($5950 × 6% × 8)
= $5950 + ($5950 ×6/100 × 8)
= $5950 + (5950 × 6 × 8/100)
= $5950 + (35700 × 8/100)
= $5950 + (285600/100)
= $5950 + $2856 = $8806
Thus, Amount (A) to be paid = $8806 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 8 years
= Simple interest for 1 year × 8
= $357 × 8 = $2856
Thus, Simple Interest (SI) = $2856
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $2856
= $8806
Thus, Amount to be paid = $8806 Answer
Similar Questions
(1) How much loan did David borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6750 to clear it?
(2) Calculate the amount due if James borrowed a sum of $3000 at 3% simple interest for 3 years.
(3) What amount does Karen have to pay after 6 years if he takes a loan of $3950 at 8% simple interest?
(4) Daniel had to pay $4469 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(5) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 8% simple interest.
(6) Daniel took a loan of $6200 at the rate of 10% simple interest per annum. If he paid an amount of $12400 to clear the loan, then find the time period of the loan.
(7) What amount does Richard have to pay after 5 years if he takes a loan of $3600 at 10% simple interest?
(8) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 9% simple interest.
(9) Calculate the amount due if Sarah borrowed a sum of $3850 at 6% simple interest for 4 years.
(10) Calculate the amount due if Patricia borrowed a sum of $3150 at 3% simple interest for 3 years.