Question:
Find the amount to be paid if Barbara borrowed a sum of $5550 at 4% simple interest for 8 years.
Correct Answer
$7326
Solution And Explanation
Solution
Given,
Principal (P) = $5550
Rate of Simple Interest (SI) = 4%
Time (t) = 8 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) = $5550 × 4% × 8
= $5550 ×4/100 × 8
= 5550 × 4 × 8/100
= 22200 × 8/100
= 177600/100
= $1776
Thus, Simple Interest = $1776
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 = $5550 + $1776
= $7326
Thus, Amount to be paid = $7326 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 = $5550
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 8 years
Thus, Amount (A)
= $5550 + ($5550 × 4% × 8)
= $5550 + ($5550 ×4/100 × 8)
= $5550 + (5550 × 4 × 8/100)
= $5550 + (22200 × 8/100)
= $5550 + (177600/100)
= $5550 + $1776 = $7326
Thus, Amount (A) to be paid = $7326 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 $5550, the simple interest in 1 year
= 4/100 × 5550
= 4 × 5550/100
= 22200/100 = $222
Thus, simple interest for 1 year = $222
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $222 × 8 = $1776
Thus, Simple Interest (SI) = $1776
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5550 + $1776
= $7326
Thus, Amount to be paid = $7326 Answer
Similar Questions
(1) Calculate the amount due after 10 years if David borrowed a sum of $5400 at a rate of 3% simple interest.
(2) William took a loan of $5000 at the rate of 7% simple interest per annum. If he paid an amount of $8500 to clear the loan, then find the time period of the loan.
(3) What amount will be due after 2 years if Michael borrowed a sum of $3150 at a 8% simple interest?
(4) What amount does David have to pay after 6 years if he takes a loan of $3400 at 9% simple interest?
(5) What amount will be due after 2 years if Matthew borrowed a sum of $3600 at a 10% simple interest?
(6) Calculate the amount due after 9 years if John borrowed a sum of $5200 at a rate of 4% simple interest.
(7) Nancy took a loan of $6300 at the rate of 8% simple interest per annum. If he paid an amount of $9324 to clear the loan, then find the time period of the loan.
(8) Mark had to pay $5060 in order to furnish the loan taken 3 years before. If the rate of simple interest was 5% then find the sum borrowed.
(9) Joseph took a loan of $5400 at the rate of 6% simple interest per annum. If he paid an amount of $7992 to clear the loan, then find the time period of the loan.
(10) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 7% simple interest?