Question:
Calculate the amount due if Sarah borrowed a sum of $3850 at 8% simple interest for 4 years.
Correct Answer
$5082
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 8%
Time (t) = 4 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) = $3850 × 8% × 4
= $3850 ×8/100 × 4
= 3850 × 8 × 4/100
= 30800 × 4/100
= 123200/100
= $1232
Thus, Simple Interest = $1232
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 = $3850 + $1232
= $5082
Thus, Amount to be paid = $5082 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 = $3850
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 4 years
Thus, Amount (A)
= $3850 + ($3850 × 8% × 4)
= $3850 + ($3850 ×8/100 × 4)
= $3850 + (3850 × 8 × 4/100)
= $3850 + (30800 × 4/100)
= $3850 + (123200/100)
= $3850 + $1232 = $5082
Thus, Amount (A) to be paid = $5082 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 $3850, the simple interest in 1 year
= 8/100 × 3850
= 8 × 3850/100
= 30800/100 = $308
Thus, simple interest for 1 year = $308
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $308 × 4 = $1232
Thus, Simple Interest (SI) = $1232
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $1232
= $5082
Thus, Amount to be paid = $5082 Answer
Similar Questions
(1) Margaret took a loan of $6700 at the rate of 6% simple interest per annum. If he paid an amount of $10318 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 3% simple interest.
(3) Find the amount to be paid if William borrowed a sum of $5500 at 2% simple interest for 8 years.
(4) Charles took a loan of $5800 at the rate of 7% simple interest per annum. If he paid an amount of $9048 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if Jessica borrowed a sum of $5750 at 6% simple interest for 8 years.
(6) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?
(7) Margaret took a loan of $6700 at the rate of 8% simple interest per annum. If he paid an amount of $10988 to clear the loan, then find the time period of the loan.
(8) Find the amount to be paid if David borrowed a sum of $5400 at 8% simple interest for 7 years.
(9) In how much time a principal of $3200 will amount to $4000 at a simple interest of 5% per annum?
(10) If Christopher paid $4320 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.