Question:
Calculate the amount due if Elizabeth borrowed a sum of $3450 at 3% simple interest for 4 years.
Correct Answer
$3864
Solution And Explanation
Solution
Given,
Principal (P) = $3450
Rate of Simple Interest (SI) = 3%
Time (t) = 4 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 3% simple interest means, Rate of Simple Interest (SI) is 3% 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 × 3% × 4
= $3450 ×3/100 × 4
= 3450 × 3 × 4/100
= 10350 × 4/100
= 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) = 3%
And, Time (t) = 4 years
Thus, Amount (A)
= $3450 + ($3450 × 3% × 4)
= $3450 + ($3450 ×3/100 × 4)
= $3450 + (3450 × 3 × 4/100)
= $3450 + (10350 × 4/100)
= $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 = 3%
This, means, $3 per $100 per year
∵ For $100, the simple interest for 1 year = $3
∴ For $1, the simple interest for 1 year = 3/100
∴ For $3450, the simple interest in 1 year
= 3/100 × 3450
= 3 × 3450/100
= 10350/100 = $103.5
Thus, simple interest for 1 year = $103.5
Therefore, simple interest for 4 years
= Simple interest for 1 year × 4
= $103.5 × 4 = $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) Find the amount to be paid if William borrowed a sum of $5500 at 10% simple interest for 8 years.
(2) Calculate the amount due after 9 years if Joseph borrowed a sum of $5700 at a rate of 3% simple interest.
(3) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 2% simple interest?
(4) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 9% simple interest?
(5) Calculate the amount due after 9 years if Mary borrowed a sum of $5050 at a rate of 3% simple interest.
(6) James took a loan of $4000 at the rate of 7% simple interest per annum. If he paid an amount of $6800 to clear the loan, then find the time period of the loan.
(7) Matthew took a loan of $6400 at the rate of 10% simple interest per annum. If he paid an amount of $12160 to clear the loan, then find the time period of the loan.
(8) How much loan did Sarah borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $7020 to clear it?
(9) If Charles paid $4524 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(10) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 5% simple interest.