Question:
What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 10% simple interest?
Correct Answer
$5775
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 10%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 10% simple interest means, Rate of Simple Interest (SI) is 10% 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 × 10% × 5
= $3850 ×10/100 × 5
= 3850 × 10 × 5/100
= 38500 × 5/100
= 192500/100
= $1925
Thus, Simple Interest = $1925
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 + $1925
= $5775
Thus, Amount to be paid = $5775 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) = 10%
And, Time (t) = 5 years
Thus, Amount (A)
= $3850 + ($3850 × 10% × 5)
= $3850 + ($3850 ×10/100 × 5)
= $3850 + (3850 × 10 × 5/100)
= $3850 + (38500 × 5/100)
= $3850 + (192500/100)
= $3850 + $1925 = $5775
Thus, Amount (A) to be paid = $5775 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 10%
This, means, $10 per $100 per year
∵ For $100, the simple interest for 1 year = $10
∴ For $1, the simple interest for 1 year = 10/100
∴ For $3850, the simple interest in 1 year
= 10/100 × 3850
= 10 × 3850/100
= 38500/100 = $385
Thus, simple interest for 1 year = $385
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $385 × 5 = $1925
Thus, Simple Interest (SI) = $1925
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $1925
= $5775
Thus, Amount to be paid = $5775 Answer
Similar Questions
(1) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 2% simple interest.
(3) Calculate the amount due if William borrowed a sum of $3500 at 9% simple interest for 4 years.
(4) How much loan did Donald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7475 to clear it?
(5) Find the amount to be paid if Linda borrowed a sum of $5350 at 7% simple interest for 8 years.
(6) Calculate the amount due after 10 years if Joseph borrowed a sum of $5700 at a rate of 6% simple interest.
(7) If Sandra paid $4806 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(8) Find the amount to be paid if Karen borrowed a sum of $5950 at 6% simple interest for 7 years.
(9) In how much time a principal of $3050 will amount to $3416 at a simple interest of 4% per annum?
(10) Find the amount to be paid if James borrowed a sum of $5000 at 9% simple interest for 7 years.