Question:
Find the amount to be paid if David borrowed a sum of $5400 at 4% simple interest for 7 years.
Correct Answer
$6912
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 4%
Time (t) = 7 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) = $5400 × 4% × 7
= $5400 ×4/100 × 7
= 5400 × 4 × 7/100
= 21600 × 7/100
= 151200/100
= $1512
Thus, Simple Interest = $1512
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 + $1512
= $6912
Thus, Amount to be paid = $6912 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) = 4%
And, Time (t) = 7 years
Thus, Amount (A)
= $5400 + ($5400 × 4% × 7)
= $5400 + ($5400 ×4/100 × 7)
= $5400 + (5400 × 4 × 7/100)
= $5400 + (21600 × 7/100)
= $5400 + (151200/100)
= $5400 + $1512 = $6912
Thus, Amount (A) to be paid = $6912 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 $5400, the simple interest in 1 year
= 4/100 × 5400
= 4 × 5400/100
= 21600/100 = $216
Thus, simple interest for 1 year = $216
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $216 × 7 = $1512
Thus, Simple Interest (SI) = $1512
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $1512
= $6912
Thus, Amount to be paid = $6912 Answer
Similar Questions
(1) In how much time a principal of $3200 will amount to $3520 at a simple interest of 5% per annum?
(2) What amount does Jessica have to pay after 5 years if he takes a loan of $3750 at 3% simple interest?
(3) James took a loan of $4000 at the rate of 6% simple interest per annum. If he paid an amount of $6160 to clear the loan, then find the time period of the loan.
(4) What amount does Michael have to pay after 5 years if he takes a loan of $3300 at 4% simple interest?
(5) Find the amount to be paid if Joseph borrowed a sum of $5700 at 7% simple interest for 8 years.
(6) Calculate the amount due if David borrowed a sum of $3400 at 9% simple interest for 4 years.
(7) What amount does Christopher have to pay after 5 years if he takes a loan of $4000 at 8% simple interest?
(8) Nancy had to pay $4399 in order to furnish the loan taken 3 years before. If the rate of simple interest was 2% then find the sum borrowed.
(9) Mary took a loan of $4100 at the rate of 9% simple interest per annum. If he paid an amount of $6314 to clear the loan, then find the time period of the loan.
(10) Find the amount to be paid if James borrowed a sum of $5000 at 2% simple interest for 8 years.