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) In how much time a principal of $3050 will amount to $3660 at a simple interest of 4% per annum?
(2) Calculate the amount due after 10 years if Robert borrowed a sum of $5100 at a rate of 8% simple interest.
(3) Find the amount to be paid if Mary borrowed a sum of $5050 at 6% simple interest for 8 years.
(4) Find the amount to be paid if Richard borrowed a sum of $5600 at 8% simple interest for 8 years.
(5) What amount does Robert have to pay after 5 years if he takes a loan of $3100 at 5% simple interest?
(6) What amount does James have to pay after 5 years if he takes a loan of $3000 at 8% simple interest?
(7) Christopher took a loan of $6000 at the rate of 6% simple interest per annum. If he paid an amount of $9240 to clear the loan, then find the time period of the loan.
(8) Calculate the amount due if Sarah borrowed a sum of $3850 at 10% simple interest for 4 years.
(9) Andrew had to pay $5088 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(10) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 8% simple interest.