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) How much loan did Amanda borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $8937.5 to clear it?
(2) Anthony took a loan of $6600 at the rate of 10% simple interest per annum. If he paid an amount of $12540 to clear the loan, then find the time period of the loan.
(3) Calculate the amount due after 10 years if Karen borrowed a sum of $5950 at a rate of 8% simple interest.
(4) What amount will be due after 2 years if Andrew borrowed a sum of $3900 at a 5% simple interest?
(5) Daniel had to pay $4346 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(6) If Michael paid $3828 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(7) Lisa took a loan of $6100 at the rate of 10% simple interest per annum. If he paid an amount of $10980 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Susan borrowed a sum of $3650 at 5% simple interest for 4 years.
(9) How much loan did Steven borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7920 to clear it?
(10) How much loan did Dorothy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $8337.5 to clear it?