Question:
Find the amount to be paid if Linda borrowed a sum of $5350 at 8% simple interest for 8 years.
Correct Answer
$8774
Solution And Explanation
Solution
Given,
Principal (P) = $5350
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) = $5350 × 8% × 8
= $5350 ×8/100 × 8
= 5350 × 8 × 8/100
= 42800 × 8/100
= 342400/100
= $3424
Thus, Simple Interest = $3424
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 = $5350 + $3424
= $8774
Thus, Amount to be paid = $8774 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 = $5350
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 8 years
Thus, Amount (A)
= $5350 + ($5350 × 8% × 8)
= $5350 + ($5350 ×8/100 × 8)
= $5350 + (5350 × 8 × 8/100)
= $5350 + (42800 × 8/100)
= $5350 + (342400/100)
= $5350 + $3424 = $8774
Thus, Amount (A) to be paid = $8774 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 $5350, the simple interest in 1 year
= 8/100 × 5350
= 8 × 5350/100
= 42800/100 = $428
Thus, simple interest for 1 year = $428
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $428 × 8 = $3424
Thus, Simple Interest (SI) = $3424
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5350 + $3424
= $8774
Thus, Amount to be paid = $8774 Answer
Similar Questions
(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 9% simple interest for 3 years.
(2) How much loan did Kimberly borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7980 to clear it?
(3) Calculate the amount due if Mary borrowed a sum of $3050 at 2% simple interest for 3 years.
(4) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 3 years.
(5) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 10% simple interest for 7 years.
(6) Christopher took a loan of $6000 at the rate of 7% simple interest per annum. If he paid an amount of $9360 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Jennifer borrowed a sum of $5250 at a rate of 3% simple interest.
(8) How much loan did Timothy borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8880 to clear it?
(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 3% simple interest for 4 years.
(10) Jennifer took a loan of $4500 at the rate of 7% simple interest per annum. If he paid an amount of $7020 to clear the loan, then find the time period of the loan.