Question:
What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 8% simple interest?
Correct Answer
$5390
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 8%
Time (t) = 5 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% × 5
= $3850 ×8/100 × 5
= 3850 × 8 × 5/100
= 30800 × 5/100
= 154000/100
= $1540
Thus, Simple Interest = $1540
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 + $1540
= $5390
Thus, Amount to be paid = $5390 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) = 5 years
Thus, Amount (A)
= $3850 + ($3850 × 8% × 5)
= $3850 + ($3850 ×8/100 × 5)
= $3850 + (3850 × 8 × 5/100)
= $3850 + (30800 × 5/100)
= $3850 + (154000/100)
= $3850 + $1540 = $5390
Thus, Amount (A) to be paid = $5390 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 5 years
= Simple interest for 1 year × 5
= $308 × 5 = $1540
Thus, Simple Interest (SI) = $1540
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $1540
= $5390
Thus, Amount to be paid = $5390 Answer
Similar Questions
(1) Calculate the amount due if William borrowed a sum of $3500 at 4% simple interest for 4 years.
(2) Christopher took a loan of $6000 at the rate of 9% simple interest per annum. If he paid an amount of $9780 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 6% simple interest?
(4) What amount does Jennifer have to pay after 6 years if he takes a loan of $3250 at 6% simple interest?
(5) Calculate the amount due if Patricia borrowed a sum of $3150 at 6% simple interest for 3 years.
(6) How much loan did Joshua borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7935 to clear it?
(7) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6300 to clear it?
(8) How much loan did Karen borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7437.5 to clear it?
(9) Calculate the amount due after 9 years if Sarah borrowed a sum of $5850 at a rate of 8% simple interest.
(10) Calculate the amount due if Christopher borrowed a sum of $4000 at 10% simple interest for 3 years.