Question:
Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
Correct Answer
$7020
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 3%
Time (t) = 10 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) = $5400 × 3% × 10
= $5400 ×3/100 × 10
= 5400 × 3 × 10/100
= 16200 × 10/100
= 162000/100
= $1620
Thus, Simple Interest = $1620
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 = $5400 + $1620
= $7020
Thus, Amount to be paid = $7020 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 = $5400
Rate of Simple Interest (SI) or (R) = 3%
And, Time (t) = 10 years
Thus, Amount (A)
= $5400 + ($5400 × 3% × 10)
= $5400 + ($5400 ×3/100 × 10)
= $5400 + (5400 × 3 × 10/100)
= $5400 + (16200 × 10/100)
= $5400 + (162000/100)
= $5400 + $1620 = $7020
Thus, Amount (A) to be paid = $7020 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 $5400, the simple interest in 1 year
= 3/100 × 5400
= 3 × 5400/100
= 16200/100 = $162
Thus, simple interest for 1 year = $162
Therefore, simple interest for 10 years
= Simple interest for 1 year × 10
= $162 × 10 = $1620
Thus, Simple Interest (SI) = $1620
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $1620
= $7020
Thus, Amount to be paid = $7020 Answer
Similar Questions
(1) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 4 years.
(2) Calculate the amount due if Joseph borrowed a sum of $3700 at 10% simple interest for 3 years.
(3) If Mary paid $3538 to settle his loan which he had taken 4 years before at a simple interest of 4%, then find the loan taken.
(4) What amount does Sarah have to pay after 6 years if he takes a loan of $3850 at 7% simple interest?
(5) Find the amount to be paid if Mary borrowed a sum of $5050 at 5% simple interest for 7 years.
(6) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 4% simple interest.
(7) Find the amount to be paid if Charles borrowed a sum of $5900 at 10% simple interest for 8 years.
(8) Elizabeth had to pay $3760.5 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(9) Karen took a loan of $5900 at the rate of 6% simple interest per annum. If he paid an amount of $9086 to clear the loan, then find the time period of the loan.
(10) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 3% simple interest?