Question:
What amount does Thomas have to pay after 6 years if he takes a loan of $3800 at 8% simple interest?
Correct Answer
$5624
Solution And Explanation
Solution
Given,
Principal (P) = $3800
Rate of Simple Interest (SI) = 8%
Time (t) = 6 years
Thus, Amount (A) = ?
The Rate of Interest is always calculated per annum, i.e. per year.
Thus, here 8% simple interest means, Rate of Simple Interest (SI) is 8% 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) = $3800 × 8% × 6
= $3800 ×8/100 × 6
= 3800 × 8 × 6/100
= 30400 × 6/100
= 182400/100
= $1824
Thus, Simple Interest = $1824
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 = $3800 + $1824
= $5624
Thus, Amount to be paid = $5624 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 = $3800
Rate of Simple Interest (SI) or (R) = 8%
And, Time (t) = 6 years
Thus, Amount (A)
= $3800 + ($3800 × 8% × 6)
= $3800 + ($3800 ×8/100 × 6)
= $3800 + (3800 × 8 × 6/100)
= $3800 + (30400 × 6/100)
= $3800 + (182400/100)
= $3800 + $1824 = $5624
Thus, Amount (A) to be paid = $5624 Answer
Method (3) Unitary Method
Calculation of Amount using Unitary Method
Calculation of Interest using Unitary Method
Here, given Rate of Simple Interest = 8%
This, means, $8 per $100 per year
∵ For $100, the simple interest for 1 year = $8
∴ For $1, the simple interest for 1 year = 8/100
∴ For $3800, the simple interest in 1 year
= 8/100 × 3800
= 8 × 3800/100
= 30400/100 = $304
Thus, simple interest for 1 year = $304
Therefore, simple interest for 6 years
= Simple interest for 1 year × 6
= $304 × 6 = $1824
Thus, Simple Interest (SI) = $1824
Calculation of Amount
Amount = Principal + Interest
Thus, Amount = $3800 + $1824
= $5624
Thus, Amount to be paid = $5624 Answer
Similar Questions
(1) Anthony took a loan of $6600 at the rate of 9% simple interest per annum. If he paid an amount of $11946 to clear the loan, then find the time period of the loan.
(2) Nancy took a loan of $6300 at the rate of 7% simple interest per annum. If he paid an amount of $10710 to clear the loan, then find the time period of the loan.
(3) Find the amount to be paid if Jennifer borrowed a sum of $5250 at 9% simple interest for 8 years.
(4) Calculate the amount due if Christopher borrowed a sum of $4000 at 7% simple interest for 3 years.
(5) How much loan did Matthew borrow 5 years ago at a rate of simple interest 5% per annum, if he paid $7750 to clear it?
(6) Calculate the amount due after 9 years if Barbara borrowed a sum of $5550 at a rate of 7% simple interest.
(7) Calculate the amount due after 10 years if Richard borrowed a sum of $5600 at a rate of 8% simple interest.
(8) In how much time a principal of $3150 will amount to $3622.5 at a simple interest of 5% per annum?
(9) Find the amount to be paid if Michael borrowed a sum of $5300 at 3% simple interest for 7 years.
(10) What amount will be due after 2 years if Donald borrowed a sum of $3750 at a 9% simple interest?