Question:
What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 3% simple interest?
Correct Answer
$4427.5
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 3%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 5
= $3850 ×3/100 × 5
= 3850 × 3 × 5/100
= 11550 × 5/100
= 57750/100
= $577.5
Thus, Simple Interest = $577.5
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 + $577.5
= $4427.5
Thus, Amount to be paid = $4427.5 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) = 3%
And, Time (t) = 5 years
Thus, Amount (A)
= $3850 + ($3850 × 3% × 5)
= $3850 + ($3850 ×3/100 × 5)
= $3850 + (3850 × 3 × 5/100)
= $3850 + (11550 × 5/100)
= $3850 + (57750/100)
= $3850 + $577.5 = $4427.5
Thus, Amount (A) to be paid = $4427.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $3850, the simple interest in 1 year
= 3/100 × 3850
= 3 × 3850/100
= 11550/100 = $115.5
Thus, simple interest for 1 year = $115.5
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $115.5 × 5 = $577.5
Thus, Simple Interest (SI) = $577.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $577.5
= $4427.5
Thus, Amount to be paid = $4427.5 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 9% simple interest.
(2) Mark had to pay $4796 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(3) Calculate the amount due if Charles borrowed a sum of $3900 at 9% simple interest for 3 years.
(4) Find the amount to be paid if Robert borrowed a sum of $5100 at 7% simple interest for 8 years.
(5) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 5% simple interest.
(6) Nancy took a loan of $6300 at the rate of 6% simple interest per annum. If he paid an amount of $8568 to clear the loan, then find the time period of the loan.
(7) Find the amount to be paid if David borrowed a sum of $5400 at 2% simple interest for 7 years.
(8) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $7172 to clear the loan, then find the time period of the loan.
(9) In how much time a principal of $3100 will amount to $3348 at a simple interest of 4% per annum?
(10) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 6% simple interest.