Question:
If Elizabeth borrowed $3450 from a bank at a rate of 2% simple interest per annum then find the amount to be paid after 2 years.
Correct Answer
$3588
Solution And Explanation
Solution
Given,
Principal (P) = $3450
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) = $3450 × 2% × 2
= $3450 ×2/100 × 2
= 3450 × 2 × 2/100
= 6900 × 2/100
= 13800/100
= $138
Thus, Simple Interest = $138
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 = $3450 + $138
= $3588
Thus, Amount to be paid = $3588 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 = $3450
Rate of Simple Interest (SI) or (R) = 2%
And, Time (t) = 2 years
Thus, Amount (A)
= $3450 + ($3450 × 2% × 2)
= $3450 + ($3450 ×2/100 × 2)
= $3450 + (3450 × 2 × 2/100)
= $3450 + (6900 × 2/100)
= $3450 + (13800/100)
= $3450 + $138 = $3588
Thus, Amount (A) to be paid = $3588 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 $3450, the simple interest in 1 year
= 2/100 × 3450
= 2 × 3450/100
= 6900/100 = $69
Thus, simple interest in 1 year = $69
Therefore, simple interest for 2 years
= Simple interest for 1 year × 2
= $69 × 2 = $138
Thus, Simple Interest (SI) = $138
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $138
= $3588
Thus, Amount to be paid = $3588 Answer
Similar Questions
(1) What amount does Jessica have to pay after 6 years if he takes a loan of $3750 at 2% simple interest?
(2) Calculate the amount due after 9 years if Thomas borrowed a sum of $5800 at a rate of 6% simple interest.
(3) Calculate the amount due after 9 years if James borrowed a sum of $5000 at a rate of 9% simple interest.
(4) Matthew took a loan of $6400 at the rate of 7% simple interest per annum. If he paid an amount of $10880 to clear the loan, then find the time period of the loan.
(5) Find the amount to be paid if John borrowed a sum of $5200 at 2% simple interest for 7 years.
(6) Find the amount to be paid if Thomas borrowed a sum of $5800 at 7% simple interest for 7 years.
(7) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 3% per annum?
(8) David took a loan of $4800 at the rate of 6% simple interest per annum. If he paid an amount of $6816 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 10% simple interest.
(10) Betty took a loan of $6500 at the rate of 9% simple interest per annum. If he paid an amount of $11180 to clear the loan, then find the time period of the loan.