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) David took a loan of $4800 at the rate of 7% simple interest per annum. If he paid an amount of $7152 to clear the loan, then find the time period of the loan.
(2) What amount does David have to pay after 6 years if he takes a loan of $3400 at 9% simple interest?
(3) Betty took a loan of $6500 at the rate of 7% simple interest per annum. If he paid an amount of $11050 to clear the loan, then find the time period of the loan.
(4) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 3% simple interest?
(5) What amount will be due after 2 years if Christopher borrowed a sum of $3500 at a 6% simple interest?
(6) Matthew had to pay $4578 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(7) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 3% simple interest.
(8) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 5% simple interest?
(9) Calculate the amount due if Richard borrowed a sum of $3600 at 5% simple interest for 3 years.
(10) What amount does Linda have to pay after 6 years if he takes a loan of $3350 at 3% simple interest?