Question:
Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 4% simple interest.
Correct Answer
$7630
Solution And Explanation
Solution
Given,
Principal (P) = $5450
Rate of Simple Interest (SI) = 4%
Time (t) = 10 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 4% simple interest means, Rate of Simple Interest (SI) is 4% 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) = $5450 × 4% × 10
= $5450 ×4/100 × 10
= 5450 × 4 × 10/100
= 21800 × 10/100
= 218000/100
= $2180
Thus, Simple Interest = $2180
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 = $5450 + $2180
= $7630
Thus, Amount to be paid = $7630 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 = $5450
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 10 years
Thus, Amount (A)
= $5450 + ($5450 × 4% × 10)
= $5450 + ($5450 ×4/100 × 10)
= $5450 + (5450 × 4 × 10/100)
= $5450 + (21800 × 10/100)
= $5450 + (218000/100)
= $5450 + $2180 = $7630
Thus, Amount (A) to be paid = $7630 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 4%
This, means, $4 per $100 per year
∵ For $100, the simple interest for 1 year = $4
∴ For $1, the simple interest for 1 year = 4/100
∴ For $5450, the simple interest in 1 year
= 4/100 × 5450
= 4 × 5450/100
= 21800/100 = $218
Thus, simple interest for 1 year = $218
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $218 × 10 = $2180
Thus, Simple Interest (SI) = $2180
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5450 + $2180
= $7630
Thus, Amount to be paid = $7630 Answer
Similar Questions
(1) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 2% simple interest?
(2) Find the amount to be paid if William borrowed a sum of $5500 at 4% simple interest for 8 years.
(3) Calculate the amount due after 10 years if Sarah borrowed a sum of $5850 at a rate of 6% simple interest.
(4) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 4% simple interest?
(5) How much loan did John borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $6240 to clear it?
(6) Sandra took a loan of $6900 at the rate of 8% simple interest per annum. If he paid an amount of $10212 to clear the loan, then find the time period of the loan.
(7) In how much time a principal of $3100 will amount to $3565 at a simple interest of 5% per annum?
(8) How much loan did Donald borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7475 to clear it?
(9) Barbara took a loan of $5100 at the rate of 6% simple interest per annum. If he paid an amount of $8160 to clear the loan, then find the time period of the loan.
(10) Calculate the amount due if Charles borrowed a sum of $3900 at 2% simple interest for 3 years.