Question:
Find the amount to be paid if Karen borrowed a sum of $5950 at 8% simple interest for 8 years.
Correct Answer
$9758
Solution And Explanation
Solution
Given,
Principal (P) = $5950
Rate of Simple Interest (SI) = 8%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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 × 8% × 8
= $5950 ×8/100 × 8
= 5950 × 8 × 8/100
= 47600 × 8/100
= 380800/100
= $3808
Thus, Simple Interest = $3808
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 + $3808
= $9758
Thus, Amount to be paid = $9758 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) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $5950 + ($5950 × 8% × 8)
= $5950 + ($5950 ×8/100 × 8)
= $5950 + (5950 × 8 × 8/100)
= $5950 + (47600 × 8/100)
= $5950 + (380800/100)
= $5950 + $3808 = $9758
Thus, Amount (A) to be paid = $9758 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $5950, the simple interest in 1 year
= 8/100 × 5950
= 8 × 5950/100
= 47600/100 = $476
Thus, simple interest for 1 year = $476
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $476 × 8 = $3808
Thus, Simple Interest (SI) = $3808
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5950 + $3808
= $9758
Thus, Amount to be paid = $9758 Answer
Similar Questions
(1) What amount does John have to pay after 5 years if he takes a loan of $3200 at 5% simple interest?
(2) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 2% simple interest?
(3) Find the amount to be paid if Michael borrowed a sum of $5300 at 4% simple interest for 7 years.
(4) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.
(5) Calculate the amount due after 9 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.
(6) If William borrowed $3500 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
(7) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.
(8) How much loan did Joseph borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6840 to clear it?
(9) How much loan did Amanda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8937.5 to clear it?
(10) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 9% simple interest.