Question:
If Sarah borrowed $3850 from a bank at a rate of 3% simple interest per annum then find the amount to be paid after 2 years.
Correct Answer
$4081
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 3%
Time (t) = 2 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% × 2
= $3850 ×3/100 × 2
= 3850 × 3 × 2/100
= 11550 × 2/100
= 23100/100
= $231
Thus, Simple Interest = $231
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 + $231
= $4081
Thus, Amount to be paid = $4081 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) = 2 years
Thus, Amount (A)
= $3850 + ($3850 × 3% × 2)
= $3850 + ($3850 ×3/100 × 2)
= $3850 + (3850 × 3 × 2/100)
= $3850 + (11550 × 2/100)
= $3850 + (23100/100)
= $3850 + $231 = $4081
Thus, Amount (A) to be paid = $4081 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 2 years
= Simple interest for 1 year × 2
= $115.5 × 2 = $231
Thus, Simple Interest (SI) = $231
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $231
= $4081
Thus, Amount to be paid = $4081 Answer
Similar Questions
(1) Lisa took a loan of $6100 at the rate of 8% simple interest per annum. If he paid an amount of $10492 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due if Barbara borrowed a sum of $3550 at 4% simple interest for 3 years.
(3) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 9% simple interest.
(4) Patricia took a loan of $4300 at the rate of 7% simple interest per annum. If he paid an amount of $6708 to clear the loan, then find the time period of the loan.
(5) What amount will be due after 2 years if William borrowed a sum of $3250 at a 9% simple interest?
(6) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $13200 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Charles borrowed a sum of $5900 at a rate of 3% simple interest.
(8) What amount does William have to pay after 6 years if he takes a loan of $3500 at 3% simple interest?
(9) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 6% simple interest.
(10) Barbara took a loan of $5100 at the rate of 7% simple interest per annum. If he paid an amount of $7956 to clear the loan, then find the time period of the loan.