Question:
Find the amount to be paid if Thomas borrowed a sum of $5800 at 4% simple interest for 7 years.
Correct Answer
$7424
Solution And Explanation
Solution
Given,
Principal (P) = $5800
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) = $5800 × 4% × 7
= $5800 ×4/100 × 7
= 5800 × 4 × 7/100
= 23200 × 7/100
= 162400/100
= $1624
Thus, Simple Interest = $1624
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 = $5800 + $1624
= $7424
Thus, Amount to be paid = $7424 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 = $5800
Rate of Simple Interest (SI) or (R) = 4%
And, Time (t) = 7 years
Thus, Amount (A)
= $5800 + ($5800 × 4% × 7)
= $5800 + ($5800 ×4/100 × 7)
= $5800 + (5800 × 4 × 7/100)
= $5800 + (23200 × 7/100)
= $5800 + (162400/100)
= $5800 + $1624 = $7424
Thus, Amount (A) to be paid = $7424 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 $5800, the simple interest in 1 year
= 4/100 × 5800
= 4 × 5800/100
= 23200/100 = $232
Thus, simple interest for 1 year = $232
Therefore, simple interest for 7 years
= Simple interest for 1 year × 7
= $232 × 7 = $1624
Thus, Simple Interest (SI) = $1624
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $5800 + $1624
= $7424
Thus, Amount to be paid = $7424 Answer
Similar Questions
(1) What amount does Christopher have to pay after 6 years if he takes a loan of $4000 at 3% simple interest?
(2) John took a loan of $4400 at the rate of 9% simple interest per annum. If he paid an amount of $6776 to clear the loan, then find the time period of the loan.
(3) Robert took a loan of $4200 at the rate of 6% simple interest per annum. If he paid an amount of $6468 to clear the loan, then find the time period of the loan.
(4) Calculate the amount due after 9 years if Jennifer borrowed a sum of $5250 at a rate of 8% simple interest.
(5) Jennifer took a loan of $4500 at the rate of 6% simple interest per annum. If he paid an amount of $7200 to clear the loan, then find the time period of the loan.
(6) Robert took a loan of $4200 at the rate of 9% simple interest per annum. If he paid an amount of $7980 to clear the loan, then find the time period of the loan.
(7) Calculate the amount due after 10 years if Elizabeth borrowed a sum of $5450 at a rate of 10% simple interest.
(8) If Jennifer paid $3640 to settle his loan which he had taken 4 years before at a simple interest of 3%, then find the loan taken.
(9) Find the amount to be paid if Karen borrowed a sum of $5950 at 5% simple interest for 8 years.
(10) Calculate the amount due if Richard borrowed a sum of $3600 at 6% simple interest for 4 years.