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) Elizabeth took a loan of $4900 at the rate of 8% simple interest per annum. If he paid an amount of $7252 to clear the loan, then find the time period of the loan.
(2) Calculate the amount due after 9 years if Linda borrowed a sum of $5350 at a rate of 7% simple interest.
(3) What amount does Susan have to pay after 6 years if he takes a loan of $3650 at 10% simple interest?
(4) Linda took a loan of $4700 at the rate of 6% simple interest per annum. If he paid an amount of $7520 to clear the loan, then find the time period of the loan.
(5) Calculate the amount due if John borrowed a sum of $3200 at 6% simple interest for 3 years.
(6) Calculate the amount due after 10 years if Jessica borrowed a sum of $5750 at a rate of 5% simple interest.
(7) Find the amount to be paid if Christopher borrowed a sum of $6000 at 5% simple interest for 8 years.
(8) Jessica took a loan of $5500 at the rate of 6% simple interest per annum. If he paid an amount of $8800 to clear the loan, then find the time period of the loan.
(9) Calculate the amount due if Barbara borrowed a sum of $3550 at 6% simple interest for 4 years.
(10) What amount does James have to pay after 6 years if he takes a loan of $3000 at 9% simple interest?