Question:
Find the amount to be paid if David borrowed a sum of $5400 at 6% simple interest for 7 years.
Correct Answer
$7668
Solution And Explanation
Solution
Given,
Principal (P) = $5400
Rate of Simple Interest (SI) = 6%
Time (t) = 7 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% × 7
= $5400 ×6/100 × 7
= 5400 × 6 × 7/100
= 32400 × 7/100
= 226800/100
= $2268
Thus, Simple Interest = $2268
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 + $2268
= $7668
Thus, Amount to be paid = $7668 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) = 7 years
Thus, Amount (A)
= $5400 + ($5400 × 6% × 7)
= $5400 + ($5400 ×6/100 × 7)
= $5400 + (5400 × 6 × 7/100)
= $5400 + (32400 × 7/100)
= $5400 + (226800/100)
= $5400 + $2268 = $7668
Thus, Amount (A) to be paid = $7668 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 7 years
= Simple interest for 1 year × 7
= $324 × 7 = $2268
Thus, Simple Interest (SI) = $2268
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5400 + $2268
= $7668
Thus, Amount to be paid = $7668 Answer
Similar Questions
(1) Calculate the amount due after 9 years if Karen borrowed a sum of $5950 at a rate of 5% simple interest.
(2) What amount does Barbara have to pay after 5 years if he takes a loan of $3550 at 6% simple interest?
(3) Calculate the amount due after 9 years if William borrowed a sum of $5500 at a rate of 6% simple interest.
(4) Christopher took a loan of $6000 at the rate of 8% simple interest per annum. If he paid an amount of $10800 to clear the loan, then find the time period of the loan.
(5) If Margaret paid $4698 to settle his loan which he had taken 4 years before at a simple interest of 2%, then find the loan taken.
(6) Calculate the amount due if Susan borrowed a sum of $3650 at 8% simple interest for 4 years.
(7) Find the amount to be paid if Joseph borrowed a sum of $5700 at 5% simple interest for 7 years.
(8) Find the amount to be paid if Susan borrowed a sum of $5650 at 7% simple interest for 7 years.
(9) In how much time a principal of $3150 will amount to $3433.5 at a simple interest of 3% per annum?
(10) What amount does Jennifer have to pay after 5 years if he takes a loan of $3250 at 6% simple interest?