Question:
If Sarah borrowed $3850 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
Correct Answer
$4004
Solution And Explanation
Solution
Given,
Principal (P) = $3850
Rate of Simple Interest (SI) = 2%
Time (t) = 2 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 2% simple interest means, Rate of Simple Interest (SI) is 2% 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 × 2% × 2
= $3850 ×2/100 × 2
= 3850 × 2 × 2/100
= 7700 × 2/100
= 15400/100
= $154
Thus, Simple Interest = $154
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 + $154
= $4004
Thus, Amount to be paid = $4004 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) = 2%
And, Time (t) = 2 years
Thus, Amount (A)
= $3850 + ($3850 × 2% × 2)
= $3850 + ($3850 ×2/100 × 2)
= $3850 + (3850 × 2 × 2/100)
= $3850 + (7700 × 2/100)
= $3850 + (15400/100)
= $3850 + $154 = $4004
Thus, Amount (A) to be paid = $4004 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 2%
This, means, $2 per $100 per year
∵ For $100, the simple interest in 1 year = $2
∴ For $1, the simple interest in 1 year = 2/100
∴ For $3850, the simple interest in 1 year
= 2/100 × 3850
= 2 × 3850/100
= 7700/100 = $77
Thus, simple interest in 1 year = $77
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $77 × 2 = $154
Thus, Simple Interest (SI) = $154
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3850 + $154
= $4004
Thus, Amount to be paid = $4004 Answer
Similar Questions
(1) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 8% simple interest.
(2) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8970 to clear it?
(3) Susan had to pay $3869 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(4) How much loan did Jennifer borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $5775 to clear it?
(5) Calculate the amount due if William borrowed a sum of $3500 at 7% simple interest for 4 years.
(6) If Sarah paid $4158 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) James took a loan of $4000 at the rate of 9% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.
(8) Margaret took a loan of $6700 at the rate of 9% simple interest per annum. If he paid an amount of $11524 to clear the loan, then find the time period of the loan.
(9) In how much time a principal of $3100 will amount to $3286 at a simple interest of 3% per annum?
(10) Calculate the amount due after 10 years if James borrowed a sum of $5000 at a rate of 8% simple interest.