Question:
What amount does Elizabeth have to pay after 6 years if he takes a loan of $3450 at 2% simple interest?
Correct Answer
$3864
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 2%
Time (t) = 6 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% × 6
= $3450 ×2/100 × 6
= 3450 × 2 × 6/100
= 6900 × 6/100
= 41400/100
= $414
Thus, Simple Interest = $414
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 + $414
= $3864
Thus, Amount to be paid = $3864 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) = 6 years
Thus, Amount (A)
= $3450 + ($3450 × 2% × 6)
= $3450 + ($3450 ×2/100 × 6)
= $3450 + (3450 × 2 × 6/100)
= $3450 + (6900 × 6/100)
= $3450 + (41400/100)
= $3450 + $414 = $3864
Thus, Amount (A) to be paid = $3864 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 for 1 year = $2
∴ For $1, the simple interest for 1 year = 2/100
∴ For $3450, the simple interest in 1 year
= 2/100 × 3450
= 2 × 3450/100
= 6900/100 = $69
Thus, simple interest for 1 year = $69
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $69 × 6 = $414
Thus, Simple Interest (SI) = $414
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3450 + $414
= $3864
Thus, Amount to be paid = $3864 Answer
Similar Questions
(1) If Joseph paid $4440 to settle his loan which he had taken 4 years before at a simple interest of 5%, then find the loan taken.
(2) How much loan did William borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $6875 to clear it?
(3) Find the amount to be paid if Barbara borrowed a sum of $5550 at 7% simple interest for 8 years.
(4) Calculate the amount due if John borrowed a sum of $3200 at 3% simple interest for 4 years.
(5) What amount will be due after 2 years if Joseph borrowed a sum of $3350 at a 9% simple interest?
(6) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 9% simple interest.
(7) How much loan did Cynthia borrow 5 years ago at a rate of simple interest 2% per annum, if he paid $8745 to clear it?
(8) David took a loan of $4800 at the rate of 9% simple interest per annum. If he paid an amount of $7824 to clear the loan, then find the time period of the loan.
(9) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 10% simple interest?
(10) Find the amount to be paid if Joseph borrowed a sum of $5700 at 10% simple interest for 7 years.