Question:
Find the amount to be paid if David borrowed a sum of $5400 at 7% simple interest for 8 years.
Correct Answer
$8424
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 7%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 7% simple interest means, Rate of Simple Interest (SI) is 7% 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 × 7% × 8
= $5400 ×7/100 × 8
= 5400 × 7 × 8/100
= 37800 × 8/100
= 302400/100
= $3024
Thus, Simple Interest = $3024
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 + $3024
= $8424
Thus, Amount to be paid = $8424 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) = 7%
And, Time (t) = 8 years
Thus, Amount (A)
= $5400 + ($5400 × 7% × 8)
= $5400 + ($5400 ×7/100 × 8)
= $5400 + (5400 × 7 × 8/100)
= $5400 + (37800 × 8/100)
= $5400 + (302400/100)
= $5400 + $3024 = $8424
Thus, Amount (A) to be paid = $8424 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 7%
This, means, $7 per $100 per year
∵ For $100, the simple interest for 1 year = $7
∴ For $1, the simple interest for 1 year = 7/100
∴ For $5400, the simple interest in 1 year
= 7/100 × 5400
= 7 × 5400/100
= 37800/100 = $378
Thus, simple interest for 1 year = $378
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $378 × 8 = $3024
Thus, Simple Interest (SI) = $3024
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $3024
= $8424
Thus, Amount to be paid = $8424 Answer
Similar Questions
(1) What amount does Joseph have to pay after 5 years if he takes a loan of $3700 at 3% simple interest?
(2) Calculate the amount due if Jessica borrowed a sum of $3750 at 7% simple interest for 3 years.
(3) Matthew had to pay $4578 in order to furnish the loan taken 3 years before. If the rate of simple interest was 3% then find the sum borrowed.
(4) Calculate the amount due if Susan borrowed a sum of $3650 at 8% simple interest for 3 years.
(5) What amount will be due after 2 years if Robert borrowed a sum of $3050 at a 7% simple interest?
(6) If Kenneth paid $5400 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(7) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 7% simple interest for 8 years.
(8) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 10% simple interest.
(9) Calculate the amount due after 10 years if Michael borrowed a sum of $5300 at a rate of 9% simple interest.
(10) In how much time a principal of $3200 will amount to $3488 at a simple interest of 3% per annum?