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) Mark took a loan of $6800 at the rate of 6% simple interest per annum. If he paid an amount of $9248 to clear the loan, then find the time period of the loan.
(2) Joseph took a loan of $5400 at the rate of 10% simple interest per annum. If he paid an amount of $9720 to clear the loan, then find the time period of the loan.
(3) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 8% simple interest?
(4) Find the amount to be paid if Jessica borrowed a sum of $5750 at 3% simple interest for 7 years.
(5) John had to pay $3680 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(6) If Michelle paid $5742 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) William took a loan of $5000 at the rate of 10% simple interest per annum. If he paid an amount of $8000 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Richard borrowed a sum of $3600 at 2% simple interest for 4 years.
(9) Lisa took a loan of $6100 at the rate of 9% simple interest per annum. If he paid an amount of $9394 to clear the loan, then find the time period of the loan.
(10) If Matthew paid $4872 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.