Question:
Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 8 years.
Correct Answer
$7992
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 6%
Time (t) = 8 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 6% simple interest means, Rate of Simple Interest (SI) is 6% 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 × 6% × 8
= $5400 ×6/100 × 8
= 5400 × 6 × 8/100
= 32400 × 8/100
= 259200/100
= $2592
Thus, Simple Interest = $2592
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 + $2592
= $7992
Thus, Amount to be paid = $7992 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) = 6%
And, Time (t) = 8 years
Thus, Amount (A)
= $5400 + ($5400 × 6% × 8)
= $5400 + ($5400 ×6/100 × 8)
= $5400 + (5400 × 6 × 8/100)
= $5400 + (32400 × 8/100)
= $5400 + (259200/100)
= $5400 + $2592 = $7992
Thus, Amount (A) to be paid = $7992 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 6%
This, means, $6 per $100 per year
∵ For $100, the simple interest for 1 year = $6
∴ For $1, the simple interest for 1 year = 6/100
∴ For $5400, the simple interest in 1 year
= 6/100 × 5400
= 6 × 5400/100
= 32400/100 = $324
Thus, simple interest for 1 year = $324
Therefore, simple interest for 8 years
= Simple interest for 1 year × 8
= $324 × 8 = $2592
Thus, Simple Interest (SI) = $2592
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $2592
= $7992
Thus, Amount to be paid = $7992 Answer
Similar Questions
(1) Susan took a loan of $5300 at the rate of 10% simple interest per annum. If he paid an amount of $10600 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 10 years if William borrowed a sum of $5500 at a rate of 9% simple interest.
(3) Matthew took a loan of $6400 at the rate of 8% simple interest per annum. If he paid an amount of $9472 to clear the loan, then find the time period of the loan.
(4) How much loan did Nancy borrow 5 years ago at a rate of simple interest 3% per annum, if he paid $7072.5 to clear it?
(5) What amount does Richard have to pay after 6 years if he takes a loan of $3600 at 6% simple interest?
(6) How much loan did Andrew borrow 5 years ago at a rate of simple interest 4% per annum, if he paid $8160 to clear it?
(7) What amount does Barbara have to pay after 6 years if he takes a loan of $3550 at 5% simple interest?
(8) Thomas took a loan of $5600 at the rate of 9% simple interest per annum. If he paid an amount of $10136 to clear the loan, then find the time period of the loan.
(9) Find the amount to be paid if Barbara borrowed a sum of $5550 at 5% simple interest for 7 years.
(10) What amount does David have to pay after 5 years if he takes a loan of $3400 at 8% simple interest?