Question:
Find the amount to be paid if David borrowed a sum of $5400 at 5% simple interest for 8 years.
Correct Answer
$7560
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 5%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 5% simple interest means, Rate of Simple Interest (SI) is 5% 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 × 5% × 8
= $5400 ×5/100 × 8
= 5400 × 5 × 8/100
= 27000 × 8/100
= 216000/100
= $2160
Thus, Simple Interest = $2160
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 + $2160
= $7560
Thus, Amount to be paid = $7560 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) = 5%
And, Time (t) = 8 years
Thus, Amount (A)
= $5400 + ($5400 × 5% × 8)
= $5400 + ($5400 ×5/100 × 8)
= $5400 + (5400 × 5 × 8/100)
= $5400 + (27000 × 8/100)
= $5400 + (216000/100)
= $5400 + $2160 = $7560
Thus, Amount (A) to be paid = $7560 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 5%
This, means, $5 per $100 per year
∵ For $100, the simple interest for 1 year = $5
∴ For $1, the simple interest for 1 year = 5/100
∴ For $5400, the simple interest in 1 year
= 5/100 × 5400
= 5 × 5400/100
= 27000/100 = $270
Thus, simple interest for 1 year = $270
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $270 × 8 = $2160
Thus, Simple Interest (SI) = $2160
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $2160
= $7560
Thus, Amount to be paid = $7560 Answer
Similar Questions
(1) What amount will be due after 2 years if Mark borrowed a sum of $3700 at a 7% simple interest?
(2) Calculate the amount due after 9 years if Charles borrowed a sum of $5900 at a rate of 10% simple interest.
(3) What amount does Karen have to pay after 5 years if he takes a loan of $3950 at 3% simple interest?
(4) Barbara took a loan of $5100 at the rate of 8% simple interest per annum. If he paid an amount of $9180 to clear the loan, then find the time period of the loan.
(5) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 7% simple interest?
(6) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 6% simple interest?
(7) Mary took a loan of $4100 at the rate of 6% simple interest per annum. If he paid an amount of $6560 to clear the loan, then find the time period of the loan.
(8) What amount does Linda have to pay after 5 years if he takes a loan of $3350 at 8% simple interest?
(9) How much loan did Thomas borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7250 to clear it?
(10) How much loan did Jeffrey borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $9360 to clear it?