Question:
What amount does Sarah have to pay after 5 years if he takes a loan of $3850 at 5% simple interest?
Correct Answer
$4812.5
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 5%
Time (t) = 5 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 5
= $3850 ×5/100 × 5
= 3850 × 5 × 5/100
= 19250 × 5/100
= 96250/100
= $962.5
Thus, Simple Interest = $962.5
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 + $962.5
= $4812.5
Thus, Amount to be paid = $4812.5 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) = 5%
And, Time (t) = 5 years
Thus, Amount (A)
= $3850 + ($3850 × 5% × 5)
= $3850 + ($3850 ×5/100 × 5)
= $3850 + (3850 × 5 × 5/100)
= $3850 + (19250 × 5/100)
= $3850 + (96250/100)
= $3850 + $962.5 = $4812.5
Thus, Amount (A) to be paid = $4812.5 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $3850, the simple interest in 1 year
= 5/100 × 3850
= 5 × 3850/100
= 19250/100 = $192.5
Thus, simple interest for 1 year = $192.5
Therefore, simple interest for 5 years
= Simple interest for 1 year × 5
= $192.5 × 5 = $962.5
Thus, Simple Interest (SI) = $962.5
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $962.5
= $4812.5
Thus, Amount to be paid = $4812.5 Answer
Similar Questions
(1) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 8% simple interest?
(2) Matthew had to pay $4704 in order to furnish the loan taken 3 years before. If the rate of simple interest was 4% then find the sum borrowed.
(3) Calculate the amount due after 9 years if Jessica borrowed a sum of $5750 at a rate of 9% simple interest.
(4) What amount will be due after 2 years if Anthony borrowed a sum of $3650 at a 5% simple interest?
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 3% simple interest for 8 years.
(6) Find the amount to be paid if Robert borrowed a sum of $5100 at 2% simple interest for 7 years.
(7) Calculate the amount due if William borrowed a sum of $3500 at 5% simple interest for 3 years.
(8) Sarah took a loan of $5700 at the rate of 6% simple interest per annum. If he paid an amount of $7752 to clear the loan, then find the time period of the loan.
(9) David took a loan of $4800 at the rate of 10% simple interest per annum. If he paid an amount of $9120 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 7 years.